Maybe, maybe not. Usually the recommendations they use are MAXIMUM sizes, so you need to pay close attention to the wording.
But you especially need to pay VERY close attention to the details of the mfrs recommendations with regard to the SCCR you can assign to the VFD. What you may find is that although they give you a recommended size for the MCCB feeding the VFD, the SCCR may require fuses, EVEN IF you have a CB. So in other words if you want to put a UL508A label on a control panel with a VFD inside, part of that will now mean including the SCCR, and the VFD without fuses will leave you with the default 5kA rating which becomes the maximum rating of your entire panel, which then means the end user basically can't install it in a typical industrial environment.
The tricky part of this is that for some of the companies that are not regularly engaged in having to deal with SCCRs and such, i.e. low cost Asian drives, the info on the SCCR is difficult to get or find. They'll toss out the recommended MCCB sizing, but leave out the details as it relates to SCCR, then you find out later when UL asks for it that you needed to add fuses. Also, it's not universally the same within each product line of each mfr, so you cannot assume anything. One product line might be fine, but that does not mean another line, or even a specific frame size WITHIN a product line, is the same.