Not from what I read a couple of months ago. The original naming rights for the stadium were a part of the clubs funding model for the stadium.
Importantly the word there is 'part'. The club also financed the stadium through other aspects such as sale of players and other available capital.
The club were quite stringent with their expenditure on players for a number of years, so that they could pay the stadium off.
Additionally, they signed up to long-term deals with major partners to help gain the original funding. This put a noose around their neck for years.
Now many of those deals have expired, and much of the stadium has been paid for, so they've been able to resign new sponsorship deals.
This includes the new more lucrative naming rights for the stadium, which now help facilitate squad building rather than funding the stadium.
They've kept Emirates because they got a very lucrative deal from them, however they could have walked away.
Now we're not in the same league of Arsenal on hospitality or advertising (based on London), but a long-term deal helped them significantly.