You can come close, but not quite. If you started from a savefile with all homeworlds unlocked via any% completion up to the point of unlocking them, the run would be very similar and contain basically all of the same tricks/tech/movement, but have some minor differences. I list the largest ones that come to mind here:
Any collectible (including dragons, which slow you down if you talk to them, so you have to avoid them) that you collected to do your any%/120% savefile would be missing from the world. In a fresh file cheat code run, all collectibles are still present in the world, and hence dragons have to generally be avoided.
The entrance to the level toasty would already be open in the savefile, assuming toasty was entered. From a fresh file you need to free a dragon after exiting another level's vortex to open the entrance to the level. With a fresh file the fastest entry is going out of bounds and entering the level from behind. With a savefile, you could just run straight in, or do the same out of bounds but enter with much more leeway. However, as far as I know you could just unlock all the homeworlds without ever opening toasty, getting around this issue.
A major difference would be the Magic Crafters balloonist Tuco. Tuco has a "catchup" mechanic where if you don't have the 5 eggs he requires to be an active balloonist, he'll warp you directly into a level that has an egg (he decides which level to offer to send you to randomly). From a savefile, Tuco's catchup mechanic would be missing, as you'd already have 5 eggs. Using the egg warp from tuco is usually fast because instead of taking you to the start of a homeworld, he drops you directly into a level with an egg. This obviously skips homeworld movement, and also a loading screen. In a savefile run you'd instead have to take the balloon normally to the peacekeepers homeworld, and traverse through it to the next level in your route.
There'll also be several whirlwinds active in levels that skip platforming that the game assumes you've already tackled, as far as I know. The ones that come to mind are Cliff Town and Lofty Castle.
Using a 120% savefile would provide an interesting quirk. Although of course it would have issues such as having the toasty head already open, it would allow access to the bonus level "Gnasty's Loot", which actually also contains a vortex. Vortex in its current form ignores this vortex, as you need 100% of the base game completed to access Gnasty's Loot. In a 120% savefile run, you could complete the "true vortex" goal of entering all the vortices in the game, instead of all but one.
Just for some final clarification, all the cheatcode used in this run actually does is make the balloonists ignore their normal collectible requirements, and allow you to select any homeworld you wish to go to straight away. Other than that, the game behaves as if you're playing from a fresh file, and even Tuco's catchup mechanic still functions, as although he's willing to take you to any homeworld, he also recognises that you don't have 5 eggs. Also several of these differences that I listed could likely be avoided by getting very specific collectibles to build the any% savefile, as if Spyro hasn't visited the areas / collected things that "matter", they'll be there as if the file was fresh.