The good news is that yes you can. The bad news is that you can only do it in a multiplayer mission. Which doesn't really matter as long as you make it clear that even though this is a mission for a single player, you have to play it in multiplayer mode. There's no problem about playing a multiplayer mission with only one human. The other bad news is that the transition is ..... inelegant.
Firstly, you need to fix your respawn options so that when the player dies he will respawn into a member of his group. This is done in the description.ext file: there are good tutorials in the Editors' Depot.
Next, create your player (west) and name him loon1
Now create a little group of east loons: make the one you want your guy to spawn into playable, which means he gets a cute pink circle round him. Call the group leader bob.
Lastly, all you really need is a trigger, fired as you will. In the on activation field put
[loon1] join bob; loon1 setdammage 1
Voila, you are now an east soldier in an east group. If you want him to lead a group you'll need to make him leave the one he is in and have his real group join him. Look at the join command in the [un]official command ref in the Editors' Depot. grpNull may come in handy too.
This is all going to be confusing for the player so make sure there is plenty of information available so he can understand what's going on.
The transition itself is pretty messy so try covering it with a cutscene, though I have a feeling that the death/respawn camerawork might overpower the cutscene. Blackout might work. If all else fails claim in the briefing that you and your twin brother were seperated at birth and landed up on different sides, but your joint spirit will never die etc etc or some other nonsense.
But Icarus is right: in SP mode there is no way.