On my machine I have two queue families, one that supports everything and one that only supports transfer.
The queue family that supports everything has a queueCount
That strongly depends on your actual scenario and setup. It's hard to tell without any details.
If you submit command buffers to multiple queues you also need to do proper synchronization, and if that's not done right you may get actually worse performance than just using one queue.
Note that even if you submit to only one queue an implementation may execute command buffers in parallel and even out-of-order (aka "in-flight"), see details on this in chapter chapter 2.2 of the specs or this AMD presentation.
If you do compute and graphics, using separate queues with simultaneous submissions (and a synchronization) will improve performance on hardware that supports async compute.
So there is no definitive yes or no on this without knowing about your actual use case.