Of course, you can imagine that. But the problems are:
1. Crucifixion was not
that common. (I know, I could hardly believe that Life Of Brian got that wrong

) It was only fairly common for runaway or rebellious slaves, bandits (and even then non-citizen bandits), etc.
2. We see in several places, including both Josephus and Acts, that the Romans actually do distinguish between political cases and local religious disputes, and that most of the local customs and laws in Judaea were solved by the local courts. When someone wants a certain James (who may or may not have been the brother of Jesus) dead, we see in Josephus that they just summon the Sanhedrin and it has that James executed. Or when John The Baptist annoys the king, said king doesn't need the Romans to execute John.
Sorry, it makes no bloody sense to have the Romans involved there. And in several places, including Acts (though that is a questionable source) that the Romans refuse to be the ones dispensing punishments at all in cases concerning local religious disputes.
Even to the authors of the Gospels, the whole episode warrants a convoluted setup where the Roman governor has his hand forced by two high priests who didn't even rule at the same time, and a hare-brained accusation of Jesus trying to proclaim himself king, that supposedly Pilate couldn't ignore. In fact, he could jolly well ignore it, if Jesus wasn't a credible threat at all. They didn't nail every single crazy guy who thought he's some religious king or messiah. And it's not clear at all why would they annoy a pretty uncooperative Roman governor, instead of just dispensing a punishment they could themselves.
3. Sorry, the whole idea of attributing something to a dead rabbi to avoid being martyred for those views, is silly, if you look at real history.
For the Romans what could get you martyred was more like:
A) denying the Gods of the state. (Merely preaching an extra God was no reason to be persecuted. You had to actually annoy the Roman by telling them their Gods are false.) And
B) treason, sedition, or other such actual crimes, by the standards of the time.
For neither of those was there an exemption if you just claimed to repeat someone else's words, regardless of whether that person was dead or alive. Attributing those ideas to Jesus would probably be the most ridiculous defense ever.
4. Roman persecution of Christians actually allowed for a far easier line of defense, than trying to convince the Judges that you're only repeating the words of an imaginary undead rabbi. At least if your only crime was denying the gods of the state.
See, the more immediate and effective defense would have been to just show that you don't. If you offered to go to the nearest shrine and offer a symbolic libation to the official god of your choice, all accusations were dropped, name cleared, you're free to go.
5. Plus, persecution was only minimal in the first century anyway. You had to make yourself pretty visible to even be accused in the first place, much less to actually end up among the single-digit number of people actually martyred. And I mean, seriously, outside of Nero's backlash after the great fire of Rome, the most you can find for any given Emperor in the 1st Century is like 1 (ONE) guy executed for religion, if even that.
Combined with the above, you probably get the idea already -- like many Roman writers also would -- that the
only people martyred, were those who actually wanted to commit suicide by the Romans' hand. The new religion promised instant saintdom to everyone who dies for their faith. If you could get the Romans to kill you, you were promised to immediately go to heaven, do not pass go, do not collect 200 denarii

So a lot of people went and trolled the Romans to get their instant guaranteed eternal reward.
Which brings us to the briefer point: all you needed to avoid getting martyred for Christianity, was to not try to get martyred. That's it.
Convoluted scenarios involving imaginary undead rabbis were simply not necessary.
6. Even more importantly, if you realize they attributed some of their own BS to a legendary rabbi Jesus, then why not all of it? How would you know which parts are true, and which are such later BS?
For that matter, if you actually believe that attributing political ideas to a dead rabbi would do anything, then why would you need a real rabbi? If you tried to avoid martyrdom in Rome, you could pretty much be assured that nobody there would know if a rabbi called Jesus actually existed before the war. So exactly why would you need a real one? Why can't you just invent a rabbi with a relatively common name -- let's call him, dunno, "Jesus" -- if you just need a mythical sockpuppet?