In order to sign any player you have to either have salary cap room, or you need to use an exception. The exception that we could use to sign Holmes that would provide salary that we expect is at least close to the salary Holmes will command is the Early Bird exception, which applies to only our own players, and only players who have been with the team for two years. The Early Bird exception, in Holmes' case, could be worth as much as about 4y/$47M. Even if we had kept CoJo instead of trading for Delon, we could not have offered Holmes more than that without renouncing free agents (all of them), because we still would not have had enough cap room to provide any value above and beyond the Early Bird exception. The Early Bird exception CANNOT be combined with cap space. You can use one, or you can use the other. Had we kept Cojo instead of Delon, AND renounced all of our free agents AND cut all of our unguaranteed money we would have been able to offer Holmes about 4y/$58M - but that would have come at the expense of at least 5 bench players and if rumors that Charlotte may offer Holmes $20M to start are true, wouldn't have come close to sealing the deal anyway.
So, Delon's money by itself could have given us enough head room under the cap to make a difference. Delon plus basically every bench player we control? Yes, a little, but at a pretty high cost.
No, if we had cap space we would not be constrained by the Early Bird amount. But as above, it would have been very difficult to get enough cap space to exceed the Early Bird value, and it would not have been exceeded by very much.
If we didn't trade for Delon, he would still be under contract to the Pistons. He would not be a free agent this offseason.