1. Yes, why not? I've carried out IMC instrument approaches to LHR in a helicopter a few times. It's difficult to get fitted in but it can be done. Can only be done in an IFR twin, of course.
2. "Infringement"? ATC have to maintain standard IFR separation between aircraft. If inadvertently going off the cleared route means that is compromised, then, yes, an infringement has occurred. It did happen a while back, an aircraft overshot a cleared waypoint near you (went too far west at 1000 feet, max height 750 feet) and standard separation was lost against an inbound to LHR, causing an investigation.