Yes, legal to weld a receiver back together for you own personal use, and since it does not need to be registered and begin built as a title 1 firearm, you can leave the serial number alone.  Truth is, your going to get more attention if you try to remove the serial number isntead.  Hence banking that the receiver in question came into the country as a parts kit, so there will be no record of the serial number on any BATF books,

As for the the firearm if this is a MG receiver, can not  fired from a open bolt position, and can not accept MG parts when you done.

If you give us an ideal of what receiver you are talking about, can walk you through the needed mods to the MG parts to get them back to title 1, and even needed mods on the receiver as you are welding it back up as well.