I know this may sound like a dumb question, but is it alright to fire 4.5mm BB's with a Winchester 1000x?

Even if you could get the bb to not roll out the barrel,it will ruin the rifleing.

I would be very careful to not fire bbs or any pellet that is to light or too heavy or to dry fire the gun.Spring action guns are very sensitive and I know from experience that bbs will break a spring action pellet gun.They are designed for an instant spring explosion,and any lack of pressure in the gun,like an unsealed bb in the barrel,will overthrow the spring,breaking it eventually.I used to have a benjamin sheridan pump,and with those,you can fire anything through them,the air pump discharging isn't affected by what is in the barrel,so I basically had a 10 bb shotgun when I felt Like it...But for spring guns,,be very careful.

...your powerplant, and scare the crap out of your neighbors because a BB will almost always go supersonic in that thing.

Ruining the barrel is a very real possibility... do it enough, and it WILL happen.

The various models that are "dual ammo" are either smoothbore (like the Marsman 1020), or have specially-designed barrels (Daisy 880).