Tag Schabette:
As saltlover said, you'll always be able to get something in the upper deck. There may be a question as to cost but if you don't need a great seat, it will likely at least be affordable.
I'm a season ticket holder and we've always had a shot at buying extras before they went on sale to the general public. My guess, and this is strictly a guess, is that most will be snapped up. A few will remain in the balcony.
Important: Is it going to be just you? You will have a much easier time getting a deal on a seat if it is a single. You'll want to look for seats that are single, or in groups of 3, 5, etc. Most people are willing to sell just an odd seat on the resale sites.
As you noted, the Celtics vary the ticket price based on the desirability of the opponent. The playoffs will work the same way, particularly since the Celtics haven't reached the second round in a while. Over the past few years, they've actually been pretty generous with pricing, pricing most of the first-round tickets at only a slight premium to in-season tickets. I seem to remember a 40% or so increase. Sorry, I normally keep a spreadsheet on these but didn't do last year's playoffs. My sheet from a few years ago says there was about a 50% jump from first to second round.
If you can't get them when they first go on sale (You likely will be able to if you sign on immediately.), here's my hint for buying them: The Celtics have an official resale site that season ticket holders are supposed to use. I use it to resell mine. But you'll probably get a better deal on Seat Geek, which is a scraper for other resale sites (although they also offer their own). The fees are lower and the variety is better. They also have a "deal score" that tells you how good the price is for particular tickets that somebody is offering. It's a guide, not a hard and fast rule.
You don't have to buy right away in the resale market. If you don't like what's available, wait it out. Prices will come down. Not a ton, but somewhat, as people who bought extra tickets realize that they won't get huge premiums for them.
Mike