Yes that would work.
The drill will break at some point but the tap should last for ages. Here is a tip from when I did metal work with my Father a good many years ago. Perhaps modern design makes this unnecessary now but it still works well.
Turn the tap one full turn in to the hole, reverse by half a turn. Forward one full turn, back a half turn - Carry on like this until the tap feels free in the hole.
The reversing clears the cut of any swarf and cleans up the thread.
Still using the Aristo tap I got years ago and purchased a pack of ten 1.5mm HSS drills from Screwfix.