Diplomacy Attacking a Territory as they move
Short answer: Yes. 

Longer answer: you can enter an area that is left by another unit. But there are some conditions.

If unit leaving the space succeeds in moving out:


if there are no other units that are ordered to enter the space, you succeed in entering it.
if there are other units ordered to enter the space, the strongest (with the most support) succeeds in entering the space, if there is a tie, nobody enters.


If the unit leaving the space fails to move out:


if there are no other units that are ordered to enter the space, you only succeed if you are stronger that the defending unit.
if there are other units ordered to enter the space, but no unit is stronger than the defending unit, the unit stays. 
if there are other units ordered to enter the space, and there is at least one unit stronger than the defending unit, the strongest unit enters. In case of a tie, the defending unit stays.


Just note that you only keep the supply center, if you occupy it during the fall phase.

And on the diplomatic level, if you trick another player like this, be prepared for revenge. So backstab wisely.

Each move has a strength. If moves conflict with other moves, the strongest move wins. In case of a tie, nothing changes.


An empty space has a strength of 0
A single defending unit has a strength of 1
A single moving unit has a strength of 1
Each unhindered support adds 1 to the strength.