what would actually happen if you fired a round like a .270 in a 30-06 chambered rifle,
What actually happens is the case expands to fit the chamber (to the limits of its ability) and the bullet goes wobbling down the barrel.
When you fire a (shorter) round with a larger caliber bullet than the bore, the same things happens, but the bullet is squeezed down in the barrel, resulting in a huge pressure spike. Sometimes enough to damage, or even destroy the gun.
.270 in an 06 is a very close fit comparatively speaking. Cases are nearly identical.
There are other combinations that fill fit and fire, some intentionally and well, (.38 SPL in .357 Mag, etc.) some that work, poorly (.270 in 06, .308 in 06, etc) and some that are dangerous.
As long as the round fits in the chamber well enough that the action can be closed, and something holds the case head against the bolt face when the gun is fired, the round will go off! What happens after that can be good, ok, meh, or OMG!!! depending on what round your firing in what chamber! And, whatever it is, it will happen, instantly!
One really needs to keep an eye on these things!