Make sure it's clear before you push yourself, but you could be ok.
I had about 10 weeks pushing myself quite hard, and then early July I developed a horrible cough, bringing up heaps of gunk and feeling rubbish. I had almost 3 weeks off the bike apart from some very short commutes.
I went back to a 25 miler into a headwind, which was very hard going, and then within a few days I found I was riding faster than I have ever done. I think the rest actually did me good. I'm glad I let it largely clear first though.