For ballpoints the answer is no. Montblanc refills are about two millimetres longer than those from Caran d'Ache, are slightly larger in diameter and have a step towards the front, so they will not even pass through the opening. Caran d'Ache refills, conversely, can be fitted into a Montblanc, but the tip then does not protrude far enough to write with the pen held at the normal angle. Both manufacturers have deliberately shaped their refills so that they do not fit other makers' pens. With Cross and Parker it was different: when their registered design protection, limited to twenty-five years, ran out, the rights were not renewed, which is why other manufacturers such as Pelikan were able to adopt these refill formats.
With rollerballs it is the other way round: the standard refills from Schmidt Feintechnik, who also make the Montblanc refills, will fit. The thread on the Montblanc refill is needed only by Montblanc barrels, and its end piece is fractionally longer, so a Montblanc refill can come under pressure in another maker's rollerball and leak.
Ink cartridges are the straightforward case: Montblanc uses the common standard format, so its cartridges fit every fountain pen that takes standard cartridges. Other makers' cartridges will likewise go mechanically into a Montblanc; the manufacturer advises against it, but in practice trouble is mainly to be expected when inks of very different composition meet in the feed.