No because modern high speed serial uses clock recovery for the timing (implemented as a first or second order PLL in the receiver), so you need to implement this in your scope too. In a real-time scope this can be done in software but in a sampling scope it has to be done in hardware and then fed into the trigger.

If you just trigger off the edges in the signal all you'll be measuring is the scope jitter.

If all you want is an eye diagram, you may not necessarily care about clock recovery, though. You'd just need a high degree of control over your own sampling clock (i.e., better than whatever you're trying to measure.)

For amplitude (the vertical part of the eye), yes. For jitter (the horizontal part), which is usually the most critical, especially for NRZ protocols like USB 3.1, no, you need clock recovery.