Yes and no.
Allowed? Probably no 1st party vendor allows/wants it.
Can do? Yeah sure.
Will I get warranty for violating some kind of EULA (or some other equivalent) for using 3rd Party? Probably not.
As an IT helpdesk we usually just tell them to get 1st party as the toner is not that expensive for that volume and just eat it. At least they have warranty for the 11k of printed papers.