Yes - conditionally.
You do not need an engineer on board - even though having one greatly helps.
The first and most important thing is to use the correct parts (the large ones):
The Convert-O-Tron 250 makes by far the biggest difference but every bit helps.
The second thing (even more important than an engineer) is the landing spot.
Mining with fuel cells on 1% ore concentration is not going to be successful. Choose your landing spot carefully to get at least around 5% concentration. The more the better.
The third most important thing is the engineer.
Given the conditions above are fulfilled you can get away with one fuel cell array per Drill-O-Matic on a mining rig that has at least four Drill-O-Matics. In this case the fuel cells can also power the Convert-O-Tron 250 and heat dissipation parts without fully maxing out its capacities.
My small mining rig has such setup and runs the 4 fuel cell arrays at 95% capacity while still producing a (small) surplus of both ore and fuel simultaneously (8% ore concentration, no engineer).
Also on inner planets fuel cells on mining rigs have the advantage of enabling mining during the night and/or greatly simplifying the setup.
Sidenote: I know that this question has a bit of dust on it but since the only answer is somewhat incorrect I chose to post an update.
The answer is technically for KSP 1.6.x but it is likely valid for all other versions > 1.0 as well as mining hasn't changed since if i remember correctly.