OK I am not positive here, but I will tell ya what I think lol. I root and ROM my phone, and never want to see an OTA, so I am not worried about if they will get pushed to my phone or not. But here is what I believe happens, or has in the past anyway. When an OTA gets pushed to your phone, a series of checks will be preformed to see if your phone is supposed to receive it and is ready to do so. When you have a heavily customized device with a custom ROM on it, you will not pass the checks and will receive no notice to install the OTA. However, if you are just rooted and that is it, it is likely you will pass the checks and the OTA will be available for download for you. In many cases, Droid X included, if you install an OTA you will lose root, so yes Bootstrap and the 3G hotspot patch will not work until you root again(which may be a long time away as with a new OTA come a need for a new root method in most cases). The exception to this case would be unrEVOked forever which allows you to keep S-OFF root access even if you do install an OTA, but that does not apply here.
As for future root dependent apps, if you install an OTA,, you will lose root so the apps will be rendered useless until you root again. I personally love Titanium Backup. It is for root users only. I flash a lot of ROMs so, besides just having a backup of apps and their respective data, I use it to reinstall certain apps after I do a wipe for a fresh ROM. For example, I use it to reinstall apps that use a personal account to easily restore without having to set up the apps again. Like Dropbox, Foursquare, Catch Notes, etc. If I re-install Catch Notes from Titanium after I flash a new ROM, the app will be loaded just as it was when I backed it up, so all my notes will already be there without having to link my account and sync my notes. Hope that makes sense.
I like to pass on OTAs and wait for one of the awesome devs to make a ROM that is based off of the OTA, lots of times basically identical. That way you won't lose root. To me, that is more important on my Droid X than it is with my Incredible as Motorola is much more strict regarding development compared to HTC. So who knows what they will sneak into an update. I like the Dev community to take a look first so I don't do something that cannot be reversed. I also like to run custom ROMs as many of them get rid of unnecessary bloatware, as well as speeding up the phone lots! Plus all the cool personal details the devs bake in. I learned development, rooting, roms, etc from my HTC Incredible which was much easier to learn on compared to the Droid X tho. But if you want to do some cool stuff with your X, there are solid ways available and plenty of helpful people to guide ya thru. If you do decide to proceed, just make sure you read the direction thru at least TWICE, BEFORE doing anything, then follow them EXACTLY, and you will be fine. Lastly, ASK QUESTIONS if you are unsure of something. If ya do that, I think you will be happy with what is available for the X, P3, DroD, and others have made some pretty damn nice, speedy and responsive ROMs, and combined with other awesome tools such as Bootstrap and ROM Manager from Koush, the X can be more awesome than you would expect
However, if you feel more comfortable with leaving your X alone, by all means do so! It is still an awesome phone!
Lastly, as I said before, the info I provided is what I am pretty sure to be true, but hopefully someone with a bit more knowledge can jump in and confirm or correct me. Enjoy!