Hello,
Actually, 90% of the aluminum that I have ever worked with has been 6061-t6 and I have never had a problem. Though I have never used 3003 before I can tell you that the reason that most extruded pieces are 6061 because of its strength, ease of welding, and overall workability. If what I have always heard was true, then aluminum does not get brittle from welding, either, but instead gets "softer". Actual physics escape me at this time, but I believe that you can expect any welds on aluminum to be weaker than that of the parent metal because of this. Do not get me wrong, I am by far no professional like you will find others on here are, but this is what I have encountered personally in numerous and extremely off the wall jobs (this includes everything from frame rails for prototype tractors to home-made popcorn poppers). Anyway, there are some great websites for weldability and workability info, and a simple search should reveal them should someone else not reply readily with them. Hope that helps!
G. L.
Here are a few factoids
Your 3003 aluminum has manganese as it's principal alloying element, as far as weldability goes there are two most favored choices for filler based on the following:
4043 is the choice for maximum strength and crack resistance
1100 is the choice for best color match after anodizing and superior ductility.
6061 (most sheet is T6) is alloyed with silicon and magnesium. Here you have 3 favored filler choices (if your not tied into manufacturers specifications.)
5356 provides maximum strength and ductility
5654 has the best color match after anodizing (I've never used this)
4043 offers the best crack resistence
Now as far as GMAW goes. If you have a push pull gun than your filler choice can be totally performance based. However, if your trying to push your wire through a short gun with a regular feeder, 5356 filler is more ridged than 4043 or 1100. Many welders have experienced great improvement in bead quality and profile just by making the switch.
As stated correctly above, welding itself should not make your 6061 brittle, but contamination, or hydrogen entrapment can, but this is true for most aluminum alloys :)
Both 3003 and 6061 are formable, just make sure your bend radii aren't too small.
Here is some good forming and general data
http://www.precisionsheetmetal.com/home/materials.htm