If I just want to check the balance of some old wallet.dat files (most likely they are all empty, but you never know), would it be OK if I launch Bitcoin Core, restore the wallet and then check the balance of the addresses in the Receiving Addresses window? Would that window show all addresses of that wallet that might contain some BTC?
If you install and let your Bitcoin Core completes its synchronisation with Bitcoin blockchain, you will see your wallet balance after that.
After sync, you can use two commands in console to check.
getbalance
getbalannces
Details on two command utility.
getbalance ( "dummy" minconf include_watchonly avoid_reuse )
Returns the total available balance.
The available balance is what the wallet considers currently spendable, and is
thus affected by options which limit spendability such as -spendzeroconfchange.
getbalances
Returns an object with all balances in BTC.