It's probably not the best idea if you want it to clear up. What I would suggest is keep your skin bare as much as possible, and if you feel you need to you can spot-cover the really unsightly ones if you are going out. NARS makes a good long-lasting concealer that comes in a lot of different shades, and you only need the tiniest bit to cover blemishes. It's a bit pricey but worth it in my opinion.
Also consider adding a honey mask to your evening skin routine. Just put a thin layer of organic honey on your face and leave it for about 30 minutes or longer. It's a natural antibacterial and will help clear up your breakouts.
You can definitely wear it, just make sure it doesn't clog pores and that it doesn't break you out. Always get a sample first. My skin is super sensitive, so only a few products suit me. I don't have acne, but I know plenty who do have it and they use foundation. You can give it a try, as others say mineral makeup is very good, but Estée Lauder double wear is also very good (but it's full coverage so it depends on what you want).
Get a mineral makeup, but make sure you get one that you don't react to. I prefer Everyday Minerals because I found out I was allergic to Bare Minerals. Mix a little of the powder foundation with your moisturizer and apply it to the face (mix it in your hand everyday rather than mixing it and leaving it in a bottle). Let it dry and then you can brush more of the powder on later to add coverage.