I am very familiar with such low level workings. On a modern, fast machine, the amount of computation required by FM synthesis is so small compared with the machine's throughput that it just doesn't matter.
Yes, on modern chips float math will generally be faster than fixed point. This is not so much because the integer units get clogged, as that there's a huge amount of chip area and optimization that goes into the float units (often SIMD, and a lot of FM synthesis can benefit from this, though feedback creates data dependencies). For example, multiply-and-add is usually one cycle in float, but would always be two separate instructions in integers.
My recollection is that older ARM chips have a special issue with latency of data dependencies originating from the float unit (NEON, which is optimized for SIMD vector operations) to the integer unit. I suspect this is no longer the case, or is less of an issue.