Nah
Forge modders use the Forge source code, that's why there is this weird legal grey area when it comes to modding.
Forgive me if you simply misspoke, but to avoid confusion I should point out that it's MCP which provides the reverse-engineered Minecraft source code for modders. FML (part of Forge) then makes it possible to load mods (including everything a coremod needs in order to parse/replace code) and provides some other lower-level API stuff for interfacing with certain objects in the game, detect other mods, etc. Forge itself then provides the higher-level API stuff for making your mod easier, primarily to interact with hooks it's implemented into various parts of Minecraft (which mods commonly use to avoid needing to be coremods), as well as things like rendering helpers and general utility code. I don't like to say that this is "all" they do, since they still do a lot for modders, but yes, this is all they do. It's not a complete Minecraft API by any means, unfortunately, which is why mods must interact so heavily with Minecraft itself, and why mods are therefore very version-dependent.
Folks might also be interested to know that the reason it's legally "okay" to distribute MCP is because it doesn't actually come with Minecraft source code when you download it. You have to run a setup script which fetches the Minecraft JAR that it needs, all of the related libraries Mojang uses, all of the media assets, etc, then starts decompiling and deobfuscating the code for you. It's a very clean process from a modder's point of view. Point-and-click, even! Then when you're ready to package your mod up, you use other scripts they included, making it very easy to compile and reobfuscate your code. They've done an awesome job making this all streamlined for mod developers. They even include a fully-configured Eclipse workspace, so that you can jump right in!
And it's also worth noting that Forge too comes with an installation script, which will in fact download MCP for you by itself, automatically run MCP's setup, then install Forge into that source code, recompile it, make sure everything works, and then you're ready to go. Again, an awesome job.
As for Mojang releasing source code, that's not entirely important. Java is relatively easy to decompile. If Minecraft weren't obfuscated, however, then modding would be significantly easier for various reasons. The obfuscation alone is what requires all of the work by the MCP team to reverse-engineer, label everything, set up the entire system of automatic deobfuscate/reobfuscate tools and mappings, make sure it recompiles properly, etc. Obfuscation is also what required you to compile your mod for every single version of the game before SRG names came out, which as I mentioned above, now automatically maps the human-readable reverse-engineered names of classes/methods/variables into the obfuscated versions, even if the obfsucated names changed between Minecraft updates. Doesn't apply to core mods or JAR mods though, since that code is still pretty much for the specific version of Minecraft that it was compiled for. And lots of mods out there still need core mods.
Essentially, obfuscation has always been the primary reason why mods need such frequent updates. But Mojang has to protect their property, even if just for legal reasons.
If it were possible for Forge to be the be-all end-all Minecraft API, where mods only ever interacted explicitly with it, then this would be less of an issue. But there's just no way they can cover every single thing that a modder might want to do in the game. So, all things considered, I would still say that the current system is still pretty amazing, even if it does mean compiling some mods for every Minecraft version.
(Holy crap I did it again with another big-ass post.)