Basically no problem. However, in some cases one can run into difficulties, 'cause a standard compliant T4P/P-Mount cart (6 g) with adaptor will already weigh a tad over 7.5 g - so, considering that most of these carts are fairly high compliance, the tonearm better shouldn't be too heavy (some 13 g max., I'd say...) in order to avoid low resonance issues. And a T4P/P-Mount cart in one of the usual adaptors will also typically be a bit higher from top to tip compared to the majority of usual MMs and MIs, namely around 20 mm instead of some 16 to 18 mm. So in some cases one might also run into VTA/SRA troubles. And besides the sonical problems, mass and height of course could also be mechanically problematic, e.g. regarding the counterweight balance range or the lift height adjustability - but these problems should be quite rare.
Greetings from Munich!
Manfred / lini