He can't, he's not bright enough to meddle with the Doctor's innards without it being obvious to B'Elanna. Or even working well enough not to totally flub up the Doc.
And that's why he loses in the love department. After spending most of your day in the intellectually stimulating presence of the Doctor wouldn't Neelix's gossip and kitchen waffle be a bore? An increasingly tedious bore. She might not fall for
the Doctor but she will fall away from Neelix with this contrast between the two having a healthy contribution to the inevitable.