In short, yes...
There are several checks that are carried out on a cycle, hour and calendar limit, whichever comes first, so obviously your cycle limit will be hit first...
{EDIT}
To clarify, there are three limits that an aircraft work to
Cycle:
One take off and landing
Hour:
Actual hours flying
Calendar:
Calendar days
You can have 3000 flights of half an hour each. This would leave you at 3000 cycles, but at 1500 hours... and so on...