Tape (at least most normal tape) won't do a good job of removing the oil. For what little it's worth, as long as you only apply it over the oily areas, the oil will probably do a pretty decent job of keeping the tape from leaving any residue behind though. The problem will arise when/if you stick the tape to parts of the lens that are currently clean (but, that's difficult to avoid).
While the glue on the tape won't peel off the coating, it stays sticky by containing solvent. Most soft/flexible plastic (like the backing of the tape) stays soft by containing some solvents as well. I don't know exactly what solvents are used in any particular brand of tape, but they're clearly not going to do the lens/coating any good.
Especially of they're left there very long, they may well do some harm. For comparison, look at a piece of paper that was taped together a long time ago. The tape will be hard, the glue no longer sticky, and (most importantly) the paper under the tape much more yellowed than the rest.
Bottom line: this will do no good. The best you can hope for is to minimize the damage it causes (and to truly minimize it, just don't do it).