No, you don’t need cache for FVM to work, it works separately from any cache.
Adding a cache plugin, basically only speeds up your HTML delivery, since WordPress doesn’t need to reprocess the page itself.
FVM merges the JS and CSS files before WP generates the page too, so it includes the newly generated static files by default, instead of the others. That means, it works with or without cache.
Nevertheless, be aware that speed optimization such as merging JS and CSS files is not a simple task, especially for ecommerce.
The simple fact of putting a bunch of JS files together can break functionality of galleries, carts, sliders, etc… hence, its important that speed optimization is done by someone with technical skills.
It’s perfectly fine to try to do it yourself for a blog or news site, but a plugin is generic. When ecommerce is involved, and thus money is involved, please make sure you test things properly once you are done (or hire a developer).
As a rule of thumb, after installing FVM or any other performance plugin, logout and test if the shop works fine. Especially, going through the checkout order process.
Most of the time it works perfectly fine, but depending on your theme and combination of plugins, you may need to work with the ignore list or other plugin options for it to work 100%.
Please understand that SEO and speed is hardly as easy as to install a plugin, although I try hard to make it as compatible with as many possible scenarios as possible.
If something is broken after you enable FVM, please try other plugins such as Autoptimize (and test again), or get someone with dev skills to help testing things.