No. MaxDop limits the number of running threads a query may have, not the total number of threads. A query running under MAXDOP 4 may have 10+ threads. Only 4 will ever be running at once. The others may be coordination threads, threads from other parallel segments that aren't running yet, etc.

To see the actual degree of parallelism, run a query with the actual execution plan included, look at the properties of a parallel operator and look at the 'Actual number of rows' property, expand it out and see how many threads are listed there.