check for datetime+period addition
- [x] closes #17983
- [x] tests added / passed
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [x] whatsnew entry

@jbrockmendel : Don't forget the `whatsnew` also :smile:  # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=h1) Report
> Merging [#18524](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/262e8ff367c9291c79c4df0c2daf4713de52abc0?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `n/a`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/18524/graphs/tree.svg?src=pr&token=eZ4WkYLtcO&width=650&height=150)](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #18524      +/-   ##
==========================================
+ Coverage   91.32%   91.33%   +<.01%     
==========================================
  Files         163      163              
  Lines       49798    49798              
==========================================
+ Hits        45479    45483       +4     
+ Misses       4319     4315       -4
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `89.13% <ø> (+0.02%)` | :arrow_up: |
| #single | `40.79% <ø> (-0.07%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/io/gbq.py](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=tree#diff-cGFuZGFzL2lvL2dicS5weQ==) | `25% <0%> (-58.34%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.81% <0%> (-0.1%)` | :arrow_down: |
| [pandas/core/indexes/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZXMucHk=) | `95.71% <0%> (+0.09%)` | :arrow_up: |
| [pandas/plotting/\_converter.py](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=tree#diff-cGFuZGFzL3Bsb3R0aW5nL19jb252ZXJ0ZXIucHk=) | `65.25% <0%> (+1.81%)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=footer). Last update [262e8ff...2d824c8](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=h1) Report
> Merging [#18524](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/262e8ff367c9291c79c4df0c2daf4713de52abc0?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `n/a`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/18524/graphs/tree.svg?width=650&height=150&src=pr&token=eZ4WkYLtcO)](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #18524      +/-   ##
==========================================
+ Coverage   91.32%   91.33%   +<.01%     
==========================================
  Files         163      164       +1     
  Lines       49798    49801       +3     
==========================================
+ Hits        45479    45485       +6     
+ Misses       4319     4316       -3
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `89.13% <ø> (+0.02%)` | :arrow_up: |
| #single | `40.81% <ø> (-0.05%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/io/gbq.py](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=tree#diff-cGFuZGFzL2lvL2dicS5weQ==) | `25% <0%> (-58.34%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.81% <0%> (-0.1%)` | :arrow_down: |
| [pandas/tseries/offsets.py](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=tree#diff-cGFuZGFzL3RzZXJpZXMvb2Zmc2V0cy5weQ==) | `96.9% <0%> (-0.05%)` | :arrow_down: |
| [pandas/util/\_test\_decorators.py](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=tree#diff-cGFuZGFzL3V0aWwvX3Rlc3RfZGVjb3JhdG9ycy5weQ==) | `95.23% <0%> (ø)` | |
| [pandas/core/indexes/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZXMucHk=) | `95.71% <0%> (+0.09%)` | :arrow_up: |
| [pandas/plotting/\_converter.py](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=tree#diff-cGFuZGFzL3Bsb3R0aW5nL19jb252ZXJ0ZXIucHk=) | `65.25% <0%> (+1.81%)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=footer). Last update [262e8ff...c79ba87](https://codecov.io/gh/pandas-dev/pandas/pull/18524?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 thanks! doesn't seem to fix: https://github.com/pandas-dev/pandas/pull/18205 but maybe helps > doesn't seem to fix: #18205 but maybe helps

Unrelated.  But that's high on my personal list, along with getting DateOffsets to be immutable.