I think there might actually be two different questions here, depending on where you are starting from.
If you have no inverter then you are running everything off DC, and running a generator for the times when you want AC. In this case I think and Inverter is a great add for most boats, providing AC power all the time rather than requiring a generator. The generator use is then reduced to heavy AC loads, and battery recharging after prolonged anchoring. It’s nearly all upside and nearly no downside.
The other question presumes an inverter, and may involve an inverter upgrade to handle larger loads. The real question is whether the addition of solar, maybe a bigger engine alternator, and maybe a wind machine can provide enough charging to eliminate the need for a generator. I think I’m most cases the answer is no, but it’s not universal. A number of people manage to fit enough solar and live in a favorable climate that makes this work, or at least enough to reduce the need for a generator to a very small percentage of time such that running the main & alternator can bridge any gaps. It’s great when it works, but from what I’ve seen most boats suffer from limited space for panels, and shading that can be minimized, but not eliminated. Also, horizontal panel mounting is often sub optimal. The result is real world performance that’s well below the nameplate ratings. Any amount is good, so I’m very much in favor of solar in boats, but you need to be cautious and realistic about what yield you will actually get.
If I were contemplating removal of a generator, I would leave it in for at least one full season with any replacement power system to assess actual performance. Then remove the generator only once you are confident the new system meets your needs.