Yes its called nested ticketing. It should work since you (presumably) aren't trying to subvert fare rules/restrictions and get lower prices. Check the T&C of your promo to make sure nested ticketing isn't explicitly excluded.

The one thing to be careful of is connection time... since they are separate tickets the system won't know that you could miss your 'connection' flight due to a delay.

Oh and this won't work if you're checking a bag, since it will end up going to the intermediate point and you'd have to go get it and recheck... unless you have a lot of time between flights to do that.