In theory, yes it's possible but I'd say it's not likely. I don't think there's enough support for it. At this stage all the EU member states are fed up of Brexit, Ireland wants closure, the Brexiteers in the UK want out as soon as possible. I think the key point to take from the article you linked to is that "the EU's chief negotiator, Michel Barnier, had advised ambassadors last week that the threat of a lengthy extension could be used by May as leverage in talks with her Brexiter MPs as she seeks to nudge the deal through parliament". Barnier and the lads are counting on the fact that those seeking to block the Withdrawal Agreement will react with horror at the possibility of remaining up to another two years in the EU. Also, when you look at the time, energy, money and resources the Brexit negotiations have already cost the UK, any responsible MP would balk at carrying on down the same road while domestic matters are sidelined and neglected.
And if the UK goes for the Article 50 extension they will have to hold European elections in May - that won't go down too well with those members of the public who voted "leave'!
I think, all in all, that's it the EU telling the UK that they can't have things the way it would suit them, with a three month extension, followed by another three months and another etc. They can have two years or nothing - and they're banking on the fact that the UK won't want want that.