Does covering a mattress with sheets prevent dust mites and their allergens?
The answer is no, normal sheets(no matter the thread count) will not keep dust mites and pollen from entering your mattress and box spring. It is possible a mattress can increase it's weight due to these two processes.
So I will assume this question to mean HOW can you cover the mattress to prevent.......
Well, for one I never take the mattress out of its original bag. It's air proof, so that covers everything else, plus it's free. I believe what you want is a vinyl plastic mattress cover. It will keep out EVERYTHING, so you're set. However any pre-existing mite colonies in the mattress will continue to eat the dust in the mattress until they die... however once you put it on, you will be separated from them hence forth.