It won't taste very cheesy if you do and it won't thicken. A good low fat cheese sauce is made with skimmed milk and cornflour to which you add a good dollop of mustard and Gruyere Cheese. The Gruyere cheese is so strong you don't need a lot of it so its lower in fat than using a normal hard cheese.
Skimmed milk, cornflour, mustard and I use parmesan as two teaspoons flavours about half a pint of sauce. I have to admit that while dieting I use the packet sauces but made up with half milk half water I know it has a few additives and salt but it is a lot cheesier.