I had glandular fever whilst serving as a boy soldier, no problem. Quick 2 weeks in camp medical station, lots of weak squash, lots of sweating and acheing but, that was it. I would say you should have no problems.
Yep you sure can, I passed the RCB medical and I had glandular fever, which progressed onto ME (not a whole barrel of laughs) Once you get a letter from you GP saying that you should have no further problems, the army are fine with it.
Hope this was of some help!