It didn't appear so.
For instance, Peter Laird's blog has no mention of it. The 1988 Playmates Toys concept art doesn't discuss it:
The toys are dated 1988, the same year as the first comic edition of the Technodrome in the Archie Comics Teenage Mutant Ninja Turtles Adventures #1. This was well after the `77 Star Wars, but there's no direct indication that Death Star was a direct inspiration.
No information is available from Kevin Eastman, the other co-creator of TMNT, on the Technodrome, either. At least, nothing that's made its way to the digital either. The same goes for Michael Dooney, the scripts and pencils guy for that first issue of TMNT Adventures.
We also see nothing from David Wise, who created many of the characters for the original 1987 TMNT cartoon show, and is credited as the creator of the Technodrome. This is interesting, because if you're going to compare the Technodrome to a giant, spherical death machine, there's a more-likely suspect:
That's the planet-mode of Unicron, a massive Transformer.
So why is Unicron a more likely suspect? Because David Wise is a well-credited writer of the G1 Transformers cartoons. He didn't appear to have involvement with the 1986 The Transformers: The Movie, where Unicron first appeared, but he did write for the show immediately before and after that. And the Season/Series 4 episodes he wrote for Transformers just so happens to have been done in 1987, which you'll note is the year before the Technodrome came out. So, was Unicron based on the Death Star? (Not based on what I can tell)
Let's get back to the Death Star, though. Once you take away the greeble and spherical likeness, the difference between the Technodrome and Death Star become much more apparent:
- The Technodrome is relatively small, not to be confused with a moon
- The Technodrome can't fly (even to Peter Laird's knowledge, it's never done so, see the blog above)
- The Technodrome has a bunch of external armaments, including tridents
- The Technodrome is mostly subterranean, not space-based
- The Technodrome has treads
- The Technodrome, for the most part, is run by one guy, Krang
So, they're very different in function and design.
Now, it's possible that Laird, Eastman or Wise could have been inspired by the massive Star Wars phenomenon, having been 23, 15 and ~22 respectively when the first film aired. But, there's no indication that they intentionally copied the concept at all. Even if it were the case, as the saying goes: The secret to creativity is knowing how to hide your sources.
There's also the chance that officially claiming the Technodrome was based off the Death Star could have led to some sort of intellectual property lawsuit, but we see no history of that. However, that could also be because large-scale production of Star Wars toys by Kenner stopped in 1985, whereas the TMNT action figures began in 1988, so there's the possibility that no one cared about suing for some extra money.
You can easily find that fans have certainly referred to the Technodrome as Death Star-like, and so have critics in recent reviews of the latest Michael Bay TMNT movie. However, that all seems to coming from viewers, not creators.