Not necessarily. It's not that the barrel is completely free to move; the barrel and slide TOGETHER are free to move backwards a certain distance before the two parts separate. The barrel and slide are locked together through that movement until the end of that distance, and can only move backwards in line with their original position. Due to Newton's 3rd law, the impulse of expanding gasses propelling the bullet act on the gun during exactly the same time, so the slide is moving backward to some degree while the bullet is still in the barrel. However, it should be gone long before the two parts SEPARATE, meaning all other things being equal, the bullet travels along its original line all the way out of the barrel and to the target, and only afterward does the barrel tilt to eject and feed.
Now, that's the theory. In practice, designers have to cut corners for reliability, durability, fit, cost, reduced recoil and other considerations. This may mean that the barrel and slide do have some play when they're supposed to be locked together, or in the extreme, the parts separate or move relative to each other before the bullet has left in order to guarantee reliable cycling. A blowback, with a fixed barrel and no off-axis motion, would not have these problems.
The "link-less" design of the Ruger P95 for instance allows a very tiny bit of play during backward travel (though with mine there's only play with no chambered round) because the camblock does not stabilize the barrel during travel as much as a linked design might. The advantage is a less jarring, smoother recoil that's better for shooter and gun. In other guns, the breech and barrel may travel backwards, but the chamber end moves downward in preparation for separation, which tilts the barrel up before the bullet has left. This increases durability as the action is less jarring to the barrel at separation, at the cost of higher shots (which can be adjusted for but is a liability in rapid fire). Still others may have a weaker recoil spring than is "ideal", as a result of age, use or design, which guarantees that the weapon will cycle properly. In the extreme, the parts may in fact move or separate before the bullet has left. This seldom happens by design and would cause far more serious problems than inaccuracy (if the bullet's still in the bore when the cartridge is extracted, the gas pressure is relieved out the ejection port, often through the cartridge wall
). Then of course there are simply guns where pricepoint is king, where tolerances might be .01" instead of .001" or .0001". It costs far less to make them and the looser tolerances, if done right, can actually increase reliability/durability, but the action will have more play than a more precision-machined weapon.
For all but the most clinical tests and the most highly-skilled shooters, the difference is generally minute; the shooter is generally a far less precise or consistent machine than the weapon. For target shooting at 200 yards, you want a gun that will always shoot exactly where the scope is pointed (allowing you to worry about where the scope is pointed and not how far off the shot will be), and in that case a fixed barrel design is inherently more accurate. But for a man-sized target at 7 yards, inherent inaccuracies of the design simply do not figure in; almost any firearm clamped on a fixed mount will literally drive tacks at that range, and the only difference is that the shooter is not a fixed mount.