You'd be wrong.
Before RA arrived, Chelsea were facing insolvency. If reports are to be believed, they were hours away from it.
They have never been in Liverpool's league and, take the regular £200M+ cash injections from their owner, they'd never be able to compete for the highest honours. No honours, massively depleted fanbase. They were on a par with West Ham, insofar as their following was concerned, pre Abramovic and the CL appearances/wins his cash afforded them.
Liverpool have become far more frugal of late, since their current owners took over really. They've spent what they've earned, with the Coutinho money spent very wisely and giving them just what they needed to win them the PL and CL. Before that, they were pretty poorly run, but they have a revenue stream afforded to them by a very large and, frankly, fanatical fanbase that isn't limited to just Liverpool. It's like putting on that Red shirt turns you into a raving lunatic!
But Chelsea would dance around the mid table without RA or a similar Billionaire, IMO that is, they simply do not have that hardcore fanbase. Once they start disappearing from CL, the gloryhunters they're inundated with will jump ship, the sponsors will do the same and their revenue drops even further.
Wouldn't all that be wonderful hey?