If Cleveland is afraid that IT will be gimpy (to use a medical term) all season, I believe a deal centered around Bledsoe becomes much more attractive to CLE. To compete, they need at least a decent PG to replace Irving. I think that is still CLE's top priority in any trade.
So if you think IT will not be a factor due to injury, suddenly Bledsoe becomes a key to the deal. Even if they won't include Josh Jackson (we won't include Tatum) they could still offer the following to correlate with our deal (and I know, salaries probably don't work but I don't think they are that far off if you assume Irving's trade kicker):
Bledsoe (Thomas)
Dudley (Crowder)
Chriss (Zizic)
Pick (BKN Pick)
Our deal is better but only if Thomas can play full speed, at least based on my interpretation of CLE's priorities. If I am Cleveland, this is not about adding another pick, unless they feel they can flip the pick for a PG (unlikely at this point), this is about getting a PG that allows them to compete now, make one more run at a title with LeBron before he goes to LA. If CLE does not believe that IT is that PG , I don't know who on the Celtics that would be. Smart? Rozier? No, I think Cleveland would want Bledsoe as their Plan B.
If CLE comes out and says we voided the deal due to IT's injury, and then makes the deal with Phoenix, there is nothing we can do. Irving might elect to not waive his kicker but so what. I know that the tax is a consideration for CLE but I think they want to win this year first and foremost.
The only other scenario that I can think of is that they want Rozier (perhaps instead of Zizic) so that Rozier can fill in for IT for the month or tow or whatever while IT is coming back. This would be if they are worried about a delay in IT's recovery but expect him back.