Not canonically. I think one of the writers is gay but said he never intended them to be a couple. If that's true is for no one to know for sure and your head canon is for no one to judge
Edit: idgaf if they're actually gay I just remember hearing a lot of people talk about that and I'm tryna figure out if it was just homophobic bullshit
They were always intended to be gay, and were based off a real life gay couple. "Really gay" was always a nudge nudge deal rather than openly admitted fact.
Frank Oz, who previously performed as Bert, stated Bert and Ernie were not gay, saying,
"They're not, of course, a gay couple. But why that question? Does it really matter? Why the need to define people as only gay? There's much more to a human being than just straightness or gayness."[17][18]
Sesame Street went on to clarify further, stating:
"No, Bert and Ernie aren't gay - they're 'best friends'".[19]
The Gaystar News reported that fans reacted negatively to this assertion. Frank Oz later tweeted in September 2018
A last thought: If Jim and I had created Bert and Ernie as gay characters they would be inauthentic, coming from two straight men. However, I have now learned that many view them as representative of a loving gay relationship. And that's pretty wonderful. Thanks for helping me understand.[20][21]
So, I would say they weren't intended that way from the start but only because the writers didn't think to do so. Frank Oz is a great reference for these things, and if he says "I love how you see them as representation" then that's good enough for me.
Bert is clearly the kind of guy who is pretty sure that Ernie is his friend, but is afraid to say it publicly on the 0.01% chance that Ernie says "we're not friends, just roommates", which would emotionally devastate Bert.