Does accrued military leave transfer to other branches?

You aren't transferring to the Army (unless you're transferring under some specific program). You will EAS from the Navy and then access into the Army. When you separate from the Navy you will have to use, sell, or lose your leave at your discharge.

Found two interesting references. An entry is directed to be made in the records of officers to provide the receiving service with a certified leave balance from the losing branch. More applicable to you, in the conditional release form for enlisted, there is a specific warning to the serviceman that they will be discharged from the losing service effective 2400 with the receiving service immediately joining them so there is no split service.
To me, the key word here is "discharged", which I would interpret as meaning you would be paid subject to normal discharge procedures. This is consistent with the difference between an enlistment contract, which is accomplished at the branch level, and a commission, which is granted by congress.
Of course, my research and opinion carries as much weight as your normal convenience store clerk, so you can either keep trying to get an answer from the pay people or go with the flow and get a surprise either way when you execute the transfer.

I went from the Navy to the Army back in 1985/6-ish and the Navy paid all the outstanding leave accrued. Clean slate with the Army. May not still be that way. Have fun in the fox holes too!