It's a good question. I think ultimately I would say no, but only because of his age. The thing is, we already missed his age 32 season this year. Really, we'd be getting age 33 LeBron and above. When we dealt for Garnett at 31 years of age, we knew the window was realistically only open a few years. LeBron would be 33 at the end of this year, and though they were both straight from HS players LeBron has so much more playoff mileage after having made like 8 finals already.
The other issue is the Cavs may prove to be sorely overmatched in this Finals. If we get LeBron our team is pretty much set and I don't think it'd be enough to beat the Warriors who will still be good for the rest of LeBron's career. Without Brown and the BKN picks, we'd have no valuable assets left to get any more useful parts. Now, if the Cavs win the Finals convincingly and LeBron is the main reason, I'd probably change my answer.
I know it may be cheating the question, but if we really were going to deal both BKN picks and Brown, we should be able to get a young star frankly. Probably not Giannis and Towns, but I have to think New Orleans wouldn't immediately hang up the phone.