Rondo has no where near the resume needed. 4 all star games, just 1 once All NBA and that was 3rd Team, though does have 4 All Defense Teams (2 each on 1st and 2nd team). No awards. He was at best the 3rd best player on the Lakers (at best) and was no better than 4th on the Celtics title team. Did lead the league 3 times for apg and once for spg (which significantly boosts his HOF Probability - see below), but never was a scorer or efficient at what little scoring he had. Solid rebounder, maybe even great for the position, but not uber elite.
That said HOF Probability has him at 60.6%, which would probably put him in the HOF, but I just don't see it. I mean Draymond Green has a better resume and he only has a 30.17% probability (Klay Thompson is 51.29% and I'd argue he has a better resume as well). Kawhi is also at just 55.56% and he clearly would make the HOF before Rondo. Rondo is getting a bit of a boost for longevity as well as those 4 stats leading the league, which is artificially making him seem like a better candidate than he actually is. Rondo needs to do a lot more to make the HOF, though I do think he has a shot if he can remain an integral part of the Lakers and if they pick up another title or two.
And while Rondo played well in game 6, for the entire finals he averaged only 8.7/5.2/5.5 on 38.8% shooting. It isn't like he was a menace for that series and really cemented himself or his candidacy. He played well, but his level of importance to the series victory was like 2% and right around KCP in level of importance (Lebron was like 55%, Davis like 40%, and the rest of the team 5%).