Personally I think it will work. An 18" rifle length barrel with regular gas port and gas block is not terribly overgassed, in fact it is the least gassed AR of the 'popular' configurations. Naturally going adjustable is a better option.
If you had asked 'can I go LW BCG with a 16" barrel and a carbine length gas system and regular gas block' I would say don't do it. But I think you'll be OK.
You'll most likely be fine. I didn't have to close the gas off much on my adjustable gas block. You could try a stiffer spring or heavier buffer but the cheapest and easiest way is an adjustable gas block.
OP, notice that both these guys still suggest the adjustable gas block is the way to go even though they say that an appropriate buffer/spring combination "should" work for you?
I also agree with them that it "should" work. The only thing is how much money are you going to spend trying different springs and/or buffer weight combinations to get the system balanced properly?
Not to mention that lighter bcg's are more sensitive to different types of ammo that will create different pressures. If, for example, you get the system tuned perfectly to a certain 5.56 round you're running and then want to switch to some lighter 223 rounds the system will react and run differently, or not at all. The adjustable gas block will allow you to make a quick and easy adjustment to compensate without the need to change anything else.
The standard spring and buffer that comes with the receiver extension will still work 100% with a lightweight bcg
if you have an adjustable gas block.
Plus the adjustable gas block will let you tune the system finer than you'll do with springs and buffers.
My .02c worth says spend the bit of extra money on an adjustable gas block and you won't regret it.
Maybe someone else will chime in here and tell you the exact parts they're using on a system like you're trying to build. But I think you can tell by the number of responses so far that the adjustable gas block just makes more sense.