They likely won't produce through the casing but if the well is successfully drilled, 2 7/8 tubing could be used if the zone is capable of high flow rates. 2 3/8 tubing is nominally used in normally pressures pay zones

Slim hole drilling will be slow due to small hole size and the inability to transmit weight to the bit with the smaller drill collar weights to crush the rock in the drilling process, but there are a few options to aid in increasing rate of penetration in slim hole driling, drill bits, stabilized BHA, etc. I believe that controlling hole angle without the use of dril collar stabilizers could present a problem if proper hoe angle to target is an issue.