It sure will.
I guarantee that ticket prices increase. Secondly, the Celtics will be able to charge more for corporate sponsorships, etc. I'm not sure when we next have to renegotiate our television deal, but that's another area of increased revenue. Also, while we don't get money from concessions, etc., I know the team gets a cut of all programs and merchandise sold on site.
The team turned a profit this year, even when paying a heavy luxury tax. I read somewhere that every dollar earned after from Game 5 of the Eastern Conference Finals onward was profit for the team, meaning that despite the heavy investment, this team brought a return.
I don't think monetary concerns will be a holdup in terms of this team attempting to improve next year. However, we only have a limited number of exceptions under the salary cap to work with, so I wouldn't expect any major spending sprees.