Can the Magic beat the Heat . . .

if they trade for Chris Paul?

Maybe.

It depends on who they get in the trade. Last year the Magic were the best team in the league, at least during the second half, because of their punishing defense. But, as you can see using the WP48 numbers, the loss of Matt Barnes to the Lakers will cost the Magic significantly.

Chris Paul is a lot better than Jameer Nelson. Switching Nelson into a backup roll and adding Paul should help the Magic win about 13 more games, which puts them 5 ahead net Barnes. 65 wins, though, is not going to be enough to compete with the Heat. (Projections for the Heat was difficult because both Lebron's and Wade's WP48 will decrease as they take less shots. Still, they should be somewhere around a 70 win team with the addition of Matt Miller and scrubs.)

To get Paul the Magic will likely lose Vince Carter and some other role players as well as, potentially, Petrius.  They are not a big loss own their own because J. J. Redick can step up and play shooting guard.

The real question for the Magic is what they are going to do at power forward. If they can acquire Emeka Okafore in the trade (to soak up his massive contract) he could be used as a significant upgrade at power forward since Rashard Lewis is the worst power forward in the league. That would net the team about 6 wins. (An alternative is to just play Gortat at power forward full time, which would net less as you lose his backup minutes.) It would also free up Lewis to play small forward since the Magic don't have a replacement for Barnes.

With all the right things happening the Magic would be a 70+ win team and be able to compete with the Heat. But if they decide to continue to play Lewis at PF they'll probably be going home in the Eastern Conference finals again next May.