It should be no problem at all - you'll just have to journey to Limsa Lominsa to the Maelstrom every time you want to set a company action or something (assuming you're authorised to set company actions by your FC leader), as those are only handled by the Grand Company of the nation that FC is allied with (in your case, the Maelstrom). Luckily this doesn't extend to using the Company chest though - you can access that in any of the three cities regardless of your GC allegiance or the FC's allegiance.