If you determine that low-flow sampling will not work in a well, can sampling still occur the same day?

If you cannot get the well to stabilize the approach in that situation is to just sample the water column that is present. Now, if you go through the low-flow protocol and drawdown continues but you have adequate sample volume, go ahead and take samples from that well, but make a note in the field log that water level stabilization could not be achieved, you will have to flag your data on that basis. You can try to identify whether or not there are other things that could have been done to get stabilization to occur.