Can disconnecting be used as a legit strategy in Dota 2 to aid your team?

Solution 1:

Based on experience and gut feeling: no, this is not a viable strategy, except perhaps in extremely unique situations. In pro play the effects of a player leaving will always be negative.

In lower level play there may be a few other things to consider why it'd be beneficial to have teammates leave:

• The player was feeding, leading enemies towards fellow teammates, or in other similar ways making the opponents stronger;
• The player may've been drawing teammates into useless chat (flame wars, etc), where they'd otherwise be doing something beneficial;

The latter actually happens a lot in low(ish) level play, I see it a lot at 3K MMR. Sometimes a player leaving brings a sort of calm to your team allowing you to focus and win after all. This is especially true if leftover players can still fill all essential roles for endgame play (control, carry).

Finally, about your last question: "Is it allowed in tournament play?". I'm no expert on official rules, but I imagine most rule sets are similar to this one from joindota, with these relevant sections (emphasis mine):

5.3 Disconnects & Reconnects

If a player disconnects, the game is to be paused instantly. Everyone has up to ten minutes to reconnect to the game (if the same person disconnects more than once, all times get added up). If this time is passed, the opposing team may continue the game, unless an admin demands the opposite. The affected player is in this case still allowed to rejoin later on.

and

5.7 Ending

A game is finished, when an Ancient Fortress is destroyed, when one team obviously forfeits, when the majority of a team leaves on purpose, or when the administration decides on it.

These rules don't really "forbid" leaving as a strategy, but from the tone you can kind of guess that it's not even remotely considered as a viable strategy.

Basically your question is similar to:

Are soccer players allowed to score an own goal to throw off their opponents mentally?

I guess it's "allowed", but the rules won't say much about this situation as there's no real way anyone'd consider it a viable strategy.