Indirectly, yes. Chelsea kicked off the spending spree we've seen over the past 20 years, with City, United etc. adding to that. With better players coming in, the stature of the league increased, thereby raising the cost of tv rights each time they are renewed.
Also, you can't say that all the PL spending over the last two decades is entirely down to an increase in TV revenue. Chelsea and City certainly didn't spend only TV money to get where they are.
Anyway, I don't think it really matters how the PL got so rich, the clubs are still buying who they want because no other Euro league bar a few elite teams can compete. I just think it's funny the Saudi's are doing to the PL what the PL do to everyone else.