Does an Alarm clock 吵醒 or 叫醒？
Yes, that is fine; it is quite common to use 叫醒 with alarms.

In fact you can use both 吵醒 and 叫醒 here, although there's a small difference in connotations. It isn't a very strong distinction though, so you needn't be overly concerned.

Anyway, 叫醒 normally means the action was intended to wake you. In contrast 吵醒 carries the sense that being woken up is unplanned or unwanted, i.e. some noise woke you (implying you aren't happy about it). For example, if your neighbours' alarm woke you, you'd normally use 吵醒. If the hotel's morning call woke you, that's normally 叫醒.