In a word, no.
Assuming we pay Rondo his qualifying offer (allowing him to become an unrestricted free agent the following season), our payroll in 2010/11 is $48,483,943.
The salary cap for the 2010/11 season should be around $65 million or so. That means we'd have $16.5 million under the cap, with four players under contract.
Now, it would be possible to make it so every other player on the team's salary expired in 2009/10. Then, theoretically, we could sign a free agent to a $16.5 million contract. However, to do so we'd have to "renounce" the rights to all of our own free agents, meaning we wouldn't be permitted to resign them for more than the league minimum.
So, we'd be in a situation where our team is:
Perk
KG
Pierce
Free Agent
Rondo
With a bench of: rookie, minimum salary player, minimum salary player, minimum salary player, minimum salary player, minimum salary player, minimum salary player.
Also, it's unlikely that Lebron would be inclined to sign here. He has a player option in 2010/11 for $17.15 million. Thus, we'd be in all likelihood be asking him to take a pay cut to come here, to play alongside two aging superstars, a talented point guard, a decent center, and a bunch of crap. When Paul and KG retired shortly thereafter, Lebron would be in a worse situation than he is now.
I just don't see it as realistic. The only way we're going to get a young, talented player in here is to hope one becomes available next offseason, at which point we can put together a package based around Ray Allen and his expiring contract. I'm not sure I want to go that route, but it's more realistic at present than trying to clear cap space.