I'm an ENT fan, but to be honest I can't say I liked the reference at all. In fact I thought it was a crap reference.
Archer was born in approx 2111, the line is said in 2261 (IIRC.) Archer would 150 years old.
McCoy was only 137 in Encounter At Farpoint, and that the was the 24th Century, and he looked like he was going to die at any minute. So how would Archer be then?
So you just basically killed a poor old mans dog? The man who saved Earth from the Xindi, who helped formed the Federation, who was dubbed 'the greatest explorer of the 22nd Century'?
That's meant to be funny?
Well, I laughed. And I'm one of the few people who liked Archer from the start of ENT. There could be all sorts of explanations why he's still alive (he got frozen, trapped in a transporter buffer, visited the Briar Patch, took a trip in the TARDIS and so on). This is science fiction, after all.
Then again, it might have been a totally different guy. It was just a nod to those who would be able to associate something with it without distracting those who never watched ENT.
I prefer to think it really was our Archer. It's a nice nod to us ENT fans. I'm content with it.
I much prefer to go by the bio from In A Mirror Darkly pt.2
, that Archer still lived pretty old, but to 2245 the day after attending the the christening ceremony of the first Federation Starship Enterprise, NCC-1701. And he wasn't an Admiral, he became Ambassador to Andoria, a councilman on the Federation, and eventually President of the UFP.
respect to the guy. Not killing off his beloved pet when he's on his deathbed
Well, this bio mentions him becoming Chief-of-Staff before being an ambassador, so he would be an admiral in that timeline, too. (It's not canon, though.)