Are single Soldiers authorized PTDY to move out of barracks?

yes if the SM has a depended or advances to the rank of SSG (some post with limited barracks SGT), as PTDY is not only for house hunting but also for moving ones Family. as per 600-8-10  

5–32. Permissive temporary duty authorization
PTDY may be authorized as follows:




f. For house hunting (absence to hunt for a house or other dwelling incident to a PCS move CONUS or OCONUS).
The following conditions apply:



(3) Soldier has unaccompanied or nonconcurrent travel entitlement to settle his or her Family at designated areas.



5–37. Rules to authorize proceed time
a. Proceed time is a nonchargeable absence for Soldiers going to or coming from an all-others overseas tour (AR
614–30).
b. Unit commander or designee is the approval authority.
c. Maximum time that may be authorized is 4 days.
d. A Soldier must be entitled to transportation of dependents or household goods or both.
e. A Soldier must actually relocate his or her dependents or household goods or both.

SGT (Join to see) - You need to read the entire 5-32 section... No PCS orders, no PDTY for house hunting.

Feel free to cite the para in 5-32 that supports PTDY is authorized for " moving ones Family."
You are looking for the para indicated by para 5-32 a through l .... You will find none of that supports PTDY may be authorized for " moving ones Family."
That is what ordinary leave is for.... and the travel time alloted is subtracted from the leave taken during PCS.
If you take 30 days "PCS" leave, and travel alloted is 10 days, you will be charged 20 days leave

But if authorized that member is eligible for BAH and COLA...