Vagabondage is a recognized word and there are dictionary entries for it. However, it is borrowed from French and it is used in French also. A more common term in English is vagrancy, as vagabond and vagrant are synonyms.
vagabondage: the state or characteristic of being a vagabond.
vagrancy: the state of being a vagrant
On the other hand, blissful vagrancy makes more sense in spiritual and religious contexts. For example, there are dervishes who choose vagrancy and practice asceticism. [Dar in Persian means "a door"; "dervish" has been interpreted as "one who goes from door to door". The Persian word also gives terms for "ascetic" in some languages, as in the Urdu phrase darveshaneh tabi'at, "an unflappable or ascetic temperament". 1]
Also, you can see the similarity between aawargi and vagari (Latin origin of vagabond and vagrant).
A vagrant or a vagabond is a person, often in poverty, who wanders from place to place without a home or regular employment or income. Other synonyms include "tramp," "hobo," and "drifter".
Both "vagrant" and "vagabond" ultimately derive from Latin word vagari "wander." The term "vagabond" is derived from Latin vagabundus. In Middle English, "vagabond" originally denoted a criminal.
In some East Asian and South Asian countries, the condition of vagrancy has long been historically associated with the religious life, as described in the religious literature of Hindu, Buddhist, Jain and Muslim Sufi traditions. Examples include sadhus, dervishes, Bhikkhus and the sramanic traditions generally.2
Google Ngram comparison between vagrancy, vagabondage and vagabondism:
In the end, vagrancy can be a near equivalent but there might not be an exact equivalent because aawargi is a combination of different aspects. As explained below based on a ghazal written by the Urdu poet Mohsin Naqvi:
A beautiful Urdu word, expressing a state of being, rather than any particular feeling. 'Aawargi' is a very difficult word to interpret, but the closest one can get to explaining it is the mind being in a state of a mystic, erratic, a trifle sexually charged, somewhat spiritual, wanderlust and finding a fulfilling solitude at the end of it all.
The term is also part of Indian culture and vagrancy is mentioned as an equivalent in the below post:
Awaara [Hindi:आवारा,Urdu:آوارہ] is a Hindi/ Urdu word which means someone away from or without a family, someone who roams around without any work etc., a wanderer, vagrant.
Awaargi or Aawaargi is the word for such state of wandering, vagrancy. The word can be heard in many songs including the one titled 'Main aur Meri Awargi' (I and My Vagrancy) sung by Kishore Kumar and then Nusrat Fateh Ali Khan. Awargi is also the title of a famous ghazal sung by Ghulam Ali.