It's not technically impossible, but it does seem incredibly unlikely that a gas planet would lack a magnetic field. This is because hydrogen (by far the most abundant element) attains metallic properties when put under extreme pressure. And a spinning metal/conductor generates magnetic fields via the dynamo effect. This is why earth has a magnetic field, except instead of metallic hydrogen spinning in our core, its our liquid iron outer core that does the trick.
Any collection of gas large enough to form a planet would certainly create the needed pressure to transform hydrogen in its metallic form. For a gas planet to have a magnetic field, it really only needs to meet 2 conditions:
- The planet needs abundant free hydrogen (which is extremely
likely given that almost all matter is hydrogen).
- The planet needs to be spinning (also extremely likely because a
planet retains the net angular momentum of all the stuff that fell
onto it while it was forming... the only way a planet avoids
spinning is by tidal locking, such as the moon always facing one
side towards the earth... and even then it's still spinning
slowly... it's just spinning once every time it completes an orbit.)
Ultimately, given the vast and possibly infinite size of the universe, and the great abundance of planets, I'd bet there is a planet somewhere that happens to be made of gasses other than hydrogen, or happens to not be rotating, and thus there would be a gas giant without a magnetosphere. But I'd be very surprised if we find one in my lifetime, or even in the the next 1000 years!