Not necessarily. Heatran is 4x weak to ground after all, and everyone thought that would be "fatal" for it defensively.
Probably the bigger issue is that the 4x weak in question, Water, is not only one of the most powerful offensive types (in terms of neutral coverage), but worse, has no immunities.
Gyarados, Tyranitar and Heatran have 4x weaknesses, but because there are immunities to electric, fighting and ground, they have teammates that can easily get around the issue. On the other hand, Dragonite has great defensive stats (and reliable recovery!), but ends up relying more on its offensive capabilities (a sweeper instead of a tank), probably in large part because Ice is not a type that any team wants to have to switch into repeatedly.
On the same note, outside Vaporeon, most teams don't want to have to deal with constantly trying to protect and switch into STAB water attacks. Even pokemon like Latias and Celebi who can shrug those attacks off easily won't like having to keep doing it, because the turns they take to recover health (and thus letting the enemy move freely for a turn) could be fatal.