Welsh Rarebit in a microwave?
When considering your options, you'll need to remember that the cheese mix must have a certain cooking time independently of the heat source:
The flour needs some time to gelatinize. Basically, the flour, butter and milk in your mix form a roux. If you heat it too short, you'll get a floury sludge instead of the cheesy creaminess you are looking for.

So while it is possible to cook the cheese sauce in the microwave, it does save neither time nor effort. You need to heat the mix slowly and stir often. If you have only a microwave at hand or are very prone to letting the cheese mix burn a bit on the stove (and detest the pot-scrubbing), it certainly is an option worth trying out. You'll need to decide for yourself, whether it fits your cooking style.



Side note re. other recipes as mentioned in other answers:
I chose to tailor my answer to your favourite recipe because even as there are lots of variations in Welsh Rarebit recipes, I assumed you like yours (with flour, sans beer or mustard) or you wouldn't call it your "staple lunch".