No, Toad is limited to one query at a time per session. However, if you select View | Toad Options | Oracle | Transactions and check "Execute queries in threads", Toad will create multiple background sessions, as needed, so more than one query can be run at a time. After checking this option, Toad may need to be restarted for it to take affect.
Toad Script Runner, a small-footprint executable that comes with Toad (snap below), can also be used to run queries. Running your scripts/queries within Script Runner (especially if they run long) won't lock up Toad panels, so you can continue your other work in Toad.
