I can only speak for LHR, but procedure-wise, it makes no difference what performance category you are, so it makes sense to report a/c type.
In fact, even if a/c category did matter, we'd probably still get you to report type as that's more important to us, for the above reasons.
If you get allocated a SID which according to your plates you cannot fly, then you should inform ATC at the time, and take reporting action to ensure the situation is resolved in the long term.