Some UPS units like the APC SMT1500 (I have a few of the Dell/EMC-branded ones) have a "Green" mode which can be enabled or disabled. When enabled, the UPS is essentially in bypass mode with most of the electronics powered down and you are connected directly to the wall until there is an event. When disabled, it operates like a normal double-conversion or AVR or etc. UPS where it essentially is running the inverter all the time and there is no direct connection to the wall, in a manner of speaking (ground is always connected of course). Also, there is a slightly longer delay before the UPS intervenes when it is in green mode due to the relay switch delay.
I've had most of my equipment on pure sine UPSs for years (in green mode) and haven't ever had any issues, but I can't say I've run any specific tests to see what things look like when the UPS is supplying the power or with green mode disabled. It probably depends on multiple factors, so running some tests would probably be the best way to determine which is better for you. I wonder if some filtering could help as well.