if you are welding sanitary connections that would need to be nsf rated (like for a commercial brewery), yes you would need to weld both sides, gas purged, and have the welds polished to prevent the buildup of crud and bacteria.
For our purposes, most people dont go thru this whole procedure and spend the extra time or money to do it. Its certainly a good thing, but the downsides of not doing it can be pretty easily mitigated. You dont really have to worry about it in your boil kettle because it will be sanitized while boiling.
The mash tun, however, could be affected by bacteria durring the mash, so making sure you clean around the welds every time is a good idea. I dont have completely sanitary welds and i have never had a problem (that i noticed). Lactobacilius bacteria do not get destroyed at 150-160 degrees, so they can live thru a mash and give you some off flavors. Normal cleaning procedures will usually take care of that. Pbw or oxiclean will kill most bacteria.
The outside is completely up to you (aesthetics only).