Telomere shortening holds one of the weakest effects on us when it comes to aging, but is very important in holding back the cancers that do not mutate the ability to regulate telomerase.
It's why im of the belief that it, as a trait, eventually ended up evolving as an anti-cancer thing, as it simply seems too convenient to be a mere happy coincidence (though it's entirely possible of course).
That said, it does technically prevent immortality, since while we have stem cells that constantly provide telomerase to our important tissues, not all of our tissues are affected by this, so on the very technical sense, deleting the ageing devil would also probably delete telomere shortening.
You do bring up a fine point though, didn't think of what if eating the ageing devil also means organisms can't grow up.
The multiplication of organisms would become conpletely impossible, and if one is pedantic, even the multiplication of tissues. Not a fun time to be a meatbag lol
Problem is if you remove ageing, you're also removing ageing for cancers. Therein lies the problem.