Server with multiple tempdb

say tempdb (the defualt one) ,temp2, temp3 and temp4.

all the 4 tempdb viz tempdb, temp2 , temp3, temp4 are part of default group.

No bindings to the any of multiple tempdbs.

Users abc logs in the server and the server assigns temp4 to the user.

While processing the request user abc fills up the temp4 temporary databasee, now will the server use any of the other available temporary database (ie tempdb,temp2,temp3) to continue the processing for the same user abc.