I don't think that will get you the result you want. If you have no other flour types in the kitchen (pancake, cake flour, maizena, etc) you could grind (very fine) a few tablespoons of dry chickpeas and use that as a substitute.
you can thicken a sauce using creamed potato, you can either do this by boiling a potato, mashing it and adding milk, then whisk it until it is the same sort of consitancy as a sauce...or...you can use instant mash potato flakes or granules which is easier.
use this mixture in the same way you would flour to thicken the butter and cheese mixture. it should result in a nice thick sauce.
Or, forget the sauce, boil the cauli until it's very tender. grate the cheese and slice an onion if you have one. put the cauli in a dish and sprinkle the rest on the top. Add any herbs you may happen to have, some black pepper is also good
stick it in the oven and you will have a lovely cheesy herby cauliflower bake with nice roasted onion. A great side dish or a main one if you serve it with some bread, rice or pasta