Remaining unmarried for the sake of worship
Question

Is marriage obligatory for a woman who is able to refrain from immoral actions all her life, in order to devote herself to her religion and to avoid the distractions and obligations of marriage?.
Praise be to Allah.Allah has enjoined marriage, as He says (interpretation of the meaning): 
“And marry those among you who are single (i.e. a man who has no wife and the woman who has no husband) and (also marry) the Saalihoon (pious, fit and capable ones) of your (male) slaves and maid-servants (female slaves). If they be poor, Allah will enrich them out of His Bounty” [al-Noor 24:32]
And it was enjoined by the Prophet (peace and blessings of Allah be upon him). It was narrated that ‘Abd-Allah ibn Mas’ood (may Allah be pleased with him) said:  The Messenger of Allah (peace and blessings of Allah be upon him) said, “O young men, whoever among you can afford it, let him get married, for it is more effective in lowering the gaze and guarding one’s chastity. And whoever cannot afford it, let him fast, for it will be a shield for him.” Narrated by al-Bukhaari, 5065; Muslim, 1400. 
And there is the story of the three men who came to ask about the worship of the Prophet (peace and blessings of Allah be upon him). When they were told about it, it was as if they thought it was not much. One of them said, “I keep away from women and I will never get married.” The Prophet (peace and blessings of Allah be upon him) said to this man and to his companions that he (peace and blessings of Allah be upon him) fasted and broke his fast, he stayed up praying and slept, and he married women. Then he said: “Whoever turns away from my Sunnah is not of me.” Narrated by al-Bukhaari, 5063; Muslim, 1401. 
This story indicates that the Prophet (peace and blessings of Allah be upon him) warned against the monasticism practiced by the Jews and Christians, both men and woman. 
So this woman should not stay unmarried. 
And Allah is the Source of strength.