From my own experience with residential VoIP and commercial VoIP solutions I have used and did tech support on; I would not recommend it if you rely on it for faxing. I just completed an intership/work-study at my school's IT dept. We just switched to a VoIP system, it has been a complete nightmare and faxes went down all over the place. Either faxes would not go through entirely or data corruption would occur. Just a plain mess.
The only solution I personally came up to fix this was to disable ECC on the fax machines. I had to fight tooth and nail to get this done since the owner of the company who was proving the service claimed that ECC needs to be on, the CIO thought we should listen to him, another dept IT thought I was an idiot. The only one who listened to me was my own supervisor; who was in charge of deploying and reporting problems with the phone system. We tried the fix on a few fax machines and they seemed to work, or we just never heard complaints back.
To make a long story short, if you want to go this route, I suggest trying it out with ECC mode disabled on the fax machine using the VoIP service before you drop your landline service altogether. Heck it doesn't even hurt to ask the VoIP provider's tech support.