A low viscosity grease would work for lubricating the internals of a switch, thus, if the mechlube2 is one, there should be no issue using it for lubricating stems indeed. I believe it was The_Ed who tried the original mechlube and reported that it was a bad idea.
Case in point - Superlube grease that I've been using for the past few months, works fine.
But the OP is basically asking if he could simply stick the syringe in and squeeze, then hope for the best in terms of improving the switch feel, without actually opening up the switches to do a proper lube job.
That will not work, because as WFD noted - grease does not flow. There's not much chance that the grease will be applied to the exact contact points required in proper switch lubing. In fact, the only way that can be done is to flood the switch with it, which is a terrible, terrible idea with grease, mainly because the grease will gunk up the entire switch.
When lubing with grease, only a thin film is required in specific locations of the switch. Oil on the other hand, will flow, but still not a great idea to flood your switches with it either, as it could leak to the pcb in the process.
TLDR, don't ghetto lube. You might get lucky, but chances are, it won't end well.