No, an SBR is an SBR. You can put a barrel of any length on an SBR, longer or shorter than what's on the form 1. As you stated, if you permanently change the configuration as written on the form 1 (read: you sell the original parts and don't have other parts to assemble to the same dimensions/caliber) you submit paperwork to amend the form 1.
Here's the typical process for SBRing an AR15 lower. We'll start with step 0:
0: Make sure you have "long" uppers for each and every "normal" lower you own. The "normal" lower you're going to SBR will be a "normal" lower until you get the Form 1 back from the ATF. For example. Lets say I own 3 ARs and I'm going to make one an SBR. I should possess 3 or more "long" uppers before I get a "short" upper (and you don't mount the short upper until you get your form 1 back). Basically you want to possess the parts such that you can put everything together in legal configurations. If you have 3 normal lowers, 2 long uppers and 1 short upper, you can't assemble everything in a legal configuration, and you can get nabbed for "constructive intent" -- that's not exactly the right term, but I forget what the correct legal term is at the moment. Just always make sure that the number of long uppers in your possession is greater than or equal to the number of normal lowers in your possession. Last example, if you have 2 normal lowers, 2 long uppers, 1 SBR and 453 short uppers you're fine, because you have enough long uppers that can be legally assembled with the normal lowers.
1: Make sure the lower is something that you want to make into an SBR. Don't just SBR a brand-new stripped receiver in case there's some defect (screwed up holes, etc.). Assemble it, make sure it runs and you're happy with it.
2: Engrave it. This way if the engraver screws up, you don't have a crappy looking re-do on your SBR.
3: Get your SBR upper (see step 0).
4: Determine barrel length. I always like to measure. Put a bolt in the upper, drop a dowel down the bore and measure it to the muzzle.
5: Determine overall length. Here you have an issue -- you can't assemble it to determine the overall length, but you can measure the lower from the the buttstock (extended) to the hinge pin, and the upper from the hinge pin hole to the muzzle and do some addition.
6: Fill out the form 1, cough up $200 and wait for six months.
O2