As worded this doesn't work, since the Comprehensive Rules say:
305.3. A player can’t play a land, for any reason, if it isn’t his or her turn. Ignore any part of an effect
that instructs a player to do so. Similarly, a player can’t play a land, for any reason, if that player
has used all of his or her land plays for that turn. Ignore any part of an effect that instructs a player
to do so.
(Incidentally this is the reason you can't play lands revealed during an opponent's turn with Djinn of Wishes.)
I'm not sure what you would have to do to make it work, but one solution would be to word it like this:
You may not play Land Dropper.

: Put Land Dropper from your hand into play. Play this ability only during an opponent's turn.

: Add

to your mana pool.
I think this card is too strong. The only time it's worse than a land that comes into play tapped and taps for colorless is if you have no other lands in your hand. It's also pretty awkward in terms of its wording. Maybe that can be improved, but it would still be too strong.
I think a reasonable version of this might be something like Gemstone Caverns, say:
Unluckyman's Grotto
Land
Reveal Unluckyman's Grotto from your hand: Put Unluckyman's Grotto from your hand into play. If you do, skip your next turn. Play this ability only during an opponent's turn.

: Add

to your mana pool.
This version has the advantage that it can be played normally, but using it to accelerate costs "a turn", which usually means a card and some untapping. Gemstone Caverns, which has a similar effect, also costs a card.
Another take in flavor with the current set mechanics would be to make it a kind of trap that could activate when opponents use fetchlands or accelerate their land drops.
Land Trap
Land
Reveal Land Trap from your hand: Put Land Trap from your hand into play. Play this ability only if an opponent has had 2 or more lands come into play this turn.

: Add

to your mana pool.