They would fight it out with Tottenham for the last spot. Bigger Club bigger fanbase world wide this would not be immediate but within years of EPL money they would attract a lot more and better players than Spurs could.
They aren't a bigger club than us because they've been playing in a pointless league for too long. Do they have more fans worldwide than us? Quick glance at the social media numbers and we dwarf them in that respect and are about to open an incredibly modern stadium which also happens to have more capacity than their own.
Add that to the fact that a vast majority of players would rather be based in London than Glasgow, the fact we're a far, far wealthier club than Celtic are (and they wouldn't catch up) who would be starting with a colossal advantage in terms of squad value, and I see no reason they would eventually overtake us.
We have the current England and French captain playing for us, but they could attract better players than us because what, they make some noise at home? There are some massive clubs in England who can't even get out of the championship, there would be no guarantee whatsoever that Celtic would break the top six.