Its important to note that many long masts are shipped in TWO pieces and sleeved together at the commissioning point! The key is it is a highly engineered solution.
As an aircraft builder and a TIG welder I'd say that, yes, a mast can be welded. Creating a hard-spot due to welding should not be too much of an issue, as the TIG welding process does not usually heat the surrounding aluminum for long enough a time to change it's qualities. Also, the area actually heated is so small to begin with that it really doesn't matter. The usual standard for welded T6 aluminum is to accept it in 'as-welded' condition.
Additionally, we are only talking about the side of the mast at the spreader. I might be concerned if we were talking about the fore side of the mast where we are dealing with tensile forces. The tensile strength of filler rod can vary around, say 37-39000 lbs and T6-aluminum (yield strength) is about 35000...but the filler strength can vary for a variety of reasons. But remember that 35000 for aluminum is the point at which it starts to deform, not bend, so I would be comfortable with the filler coming in at the low end, even slightly below the yield strength of the base aluminum mast. At 35000 lbs the whole mast might come down anyways.
In welding I would worry more about breaking strength than the bending forces initially. A good weld just isn't going to break. Usually the metal will go before the filler...in a good weld. A good weld is no different than, say, drilling a hole in the mast and then putting in a tight bolt. The aluminum filler rod will generate less of a 'hard spot' than a stainless steel bolt. Another thing too, we're not talking about a complete circumferential weld...but that's what sleeving a mast together is for... If a big sleeve doesn't cause a problem a TIG weld won't either.
Last..you shouldn't have to bring the mast in...but the welder might need a wooden ladder to stand on so as not to complete the circuit between the 'torch' and the mast. The voltage of TIG can be dangerous if not careful.