Yes and we do it a lot. We are often cleared for a visual approach to a runway. That means we almost responsible for our own traffic separation and in the event of a go around, we will continue to see and avoid other aircraft.
Most airline operations manuals say we must use all available guidance so that means we’re supposed to tune and monitor an instrument approach procedure. The workaround is to have the non-flying pilot do that part while the flying pilot just flys the approach and landing just like a small airplane flown by a private pilot.
it’s good practice to stay comfortable with this method but mostly it’s fun and amost all of us enjoy flying a visual approach without any electronic guidance. It feels kind of free and easy and fun to just look out the windshield and fly. I like it and sadly it’s not always possible even in good weather because of high traffic.
Some will say that modern pilots are overly dependent upon electronic guidance but I disagree. I’ve noticed in the last 10 years that the copilots are punching off the autopilot much earlier and hand flying far more than when I started with the airlines in the mid 80’s. The older pilots back then used the autopilot all the way to short final almost all the time. Watching them from my engineers seat was interesting and I didn’t expect the old guys to be so dependent on the autopilot. I don’t know what has changed but the younger generation has adopted a policy of hand flying a lot more than the older generation and I think it’s a good thing.
Edit 1: I assumed the person posting this question was talking about electronic flight guidance and not the airspeed indicator, compass or altimeter. I think I take those instruments for granted because I’ve never flown an aircraft without them (except a paraglider). If that’s what the poster intended, then the answer would be “no”.
We never make an approach without airspeed, altimeter and heading. It’s possible and there is a checklist for flying without an airspeed indicator and it has a table for power settings and pitch angles at various weights. I’ve done it in the simulator a grand total of one time. It worked but it wasn’t pretty. It would be very irresponsible to cover the airspeed indicator and try to land an airliner.