Technically, yes. But not because of the 2kHz carrier, although that does have an effect, but rather because the devices are technically rated for 50/60 Hz operation, so using them at anything less is a 110.3 violation.
In reality, the high CF and harmonic rich output of a VFD can cause additional heating in bi-metal current sensing elements, such as OL relays and thermal trips on CBs and MPCBs. So what can happen is not failure to trip but rather nuisance tripping. Then the problem become the human response to nuisance tripping; turning up the dial, which then exposes a risk of it NOT tripping when there really is an overload. Side note: the old eutectic melting alloy OL relays are rated for operation at any frequency up to 400Hz.
Some suppliers are now making protective devices tested and listed for use behind VFDs. A-B now has a version of their 140M Motor Protection Circuit Breakers called the “D8V” that is specifically rated for use down stream of VFDs. I’ve heard others are offering that too or will be soon.