Is permissive TDY being granted during COVID-19 to soldiers leaving AIT with dependents?

Talk to your chain of command

Be sure to check with the inprocessing section at your upcoming duty station. Under the “Newcomers” section of the post website, see if you can find the phone number for the building/location where you are required to sign in off leave. They can probably tell you how local policy affects permissive TDY. Some installations have a policy of immediately signing you out on PTDY upon arrival. Some require you to finish inprocessing first. A few installations also still require PTDY to be granted by your new chain of command, but that has become less common.

Permissive TDY also known as leave for house hunting is exactly what it sounds like. You have 10 days to secure a lease. Once lease is secured, you are required to sign back in. Its not just free leave to do what you want. Your wife being pregnant does not affect nor justify being given PTDY. Must inprocess your duty station and be arrived at your unit before PTDY is authorized.

You can get permissive TDY for a lot of things however moving your wife is not one of them. There will be no more PTDY after 16 AUG and it will be called administrative absence. Go here and find 600-8-10:https://armypubs.army.mil . You want the one dated 2020 as both old and new are still up. If she is 27 weeks, she is still 13 weeks from her due date and should be able to travel into Sept unless she is high risk. Speak with her OB about travel. To answer your question, there is no block on administrative absence and you should get some time for house hunting after AIT. Check out the reg.