Q:

Did Mother Sati become a ghost after committing sucide?

This answer states that after suicide a person becomes a ghost. Then did mother Sati become ghost after committing suicide?

A:

Mother Sati is not an ordinary mortal governed by the laws of jeeva, life and death. She did not commit "suicide". She forsook her upadhi using powers of yoga. 
Even among mortals,  Highly evolved souls(I. E advanced yogis)  are capable of separating their soul from the body. In those who are not as evolved, the jeeva is almost inextricably tied to the upadhi, which is why even natural deaths are said to be painful. Suicide is the act of forcibly separating the jeeva from the upadhi. 
Coming back to Sati devi, she gave up her form but still existed as Lord Shiva's jnana sakti when He  assumed the jnana form after separation from Sati. 

A:

Mother Sati gave up her body through the process of Kundalini Yoga. And leaving the body through the path of Yoga is not called Suicide. Here is how Srimad Bhagvatam
describes the event:

इत्यध्वरे दक्षमनूद्य शत्रुहन्क्षितावुदीचीं निषसाद शान्तवाक् । स्पृष्टा जलं पीतदुकूलसंवृतानिमील्य द्दग्योगपथं समाविशत् ।। कृत्वा समानावनिलौ जितासना सोदानमुत्थात्य च नाभिचक्रतः । शनैर्ह्र्दि स्थात्य धियोरसि स्थितं कण्ठाद्भ्रुवोर्मध्यमनिन्दितानयत् ।।
  एवं स्वदेह महतां महीयसा मुहुः समारोपितमंकमादरात् ।
  जिहासती दक्षरुषा मनस्विनी दधार गात्रेष्वनिलाग्निधारणाम् ।। ततः स्वभर्तश्चरणाम्बुजासवं जगद्गुरोश्र्चिन्तयति न चापरम् । ददर्श देहो हतकल्मषः सती सद्यः प्रजज्वाल समाधि जाग्निना ।। [S.B. 4.4.24-27]

  O annihilator of enemies, while thus speaking to her father in the arena of sacrifice, Satī sat down on the ground and faced north. Dressed in saffron garments, she sanctified herself with water and closed her eyes to absorb herself in the process of mystic yoga. First of all she sat in the required sitting posture, and then she carried the life air upwards and placed it in the position of equilibrium near the Nabhi Chakra [Manipura Chakra]. Then she raised her life air, mixed with intelligence, to the heart [Anhata Chakra] and then gradually towards the pulmonary passage, to the throat [Visuddha Chakra] and from there to between her eyebrows [Ajna Chakra]. Thus, in order to give up her body, which had been so respectfully and affectionately seated on the lap of Lord Śhiva, who is worshiped by great sages and saints, Satī, due to anger towards her father, began to meditate on the fiery air within the body. Satī concentrated all her meditation on the holy lotus feet of her husband, Lord Śhiva, who is the supreme spiritual master of all the world. Thus she became completely cleansed of all taints of sin and quit her body in a blazing fire by meditation on the fiery elements.

Thus from above it is clear she left her body through path of highly mystic yoga. And furthermore she is always with SadaShiva in her true form Amba and also represented as Samba-SadaShiva. She took birth latter from Menavati as Parvati and again married to Lord Shankara.

