No. There is a caveat here, that a proper heat treatment for 6061 involves a heat-and-quench step to maximize the hardening *potential* of the aluminum, but the actual hardening occurs later and has nothing directly to do with quenching. The purpose of quenching aluminum alloys is to "freeze" alloying elements in the metal, in a solid solution. The actual hardening is accomplished by precipitation hardening, which occurs naturally by room-temperature aging, or more quickly with a low-temp heat-soak process known as artificial aging. Most heat-treatable aluminum alloys can achieve a moderate or even a large fraction of their potential hardness without the heat-and-quench step. IIRC, 6061 is one of those that achieves most of its potential hardness without quenching, but I haven't refreshed my memory on this for a while.
If this is a critical job, you'd do well to study it a bit. 6xxx-series aluminum that's randomly heat-treated, as by welding, continues to age for years and is never really stable. 2xxx aluminum, in contrast, will stabilize within a week. But 2024, for example, is risky to weld, usually producing high-stress areas and even cracks. 6061 is much less trouble and is far better for welding.
Few applications require the highest levels of strength or long-term stability, so welding 6061 usually is not a problem. Just weld and wait. Within a week or so it will have recovered a substantial percentage of its strength. I wouldn't try quenching it because the required heat-and-quench to achieve maximum hardness is time-and-temperature sensitive. If you can't control both and know exactly what values of time and temperature you need, heating and quenching can make things worse.
Don't try to relate it to hardening carbon steel. The hardening mechanisms are entirely different.
When prepping the weld area, any grinding wheels (to taper the edge where the weld will go) or stainless wire wheels the welder uses should be either new or if used, only used on aluminum previously, yes?
I think I remember an issue of contamination of ferrous material getting imbedded into the aluminum if precautions are not taken.
Oops. I didn't know it was a bike frame. That's a job I'd consider to be fairly critical. In fact, it will be interesting to see what the welding experts say.
I'm a materials guy, Dave, but only a klutzy weldor. If it were me I'd check with the people at the welding NG, which is a source of some real welding expertise. Also, there is a bicycling NG that's been home to some bike-building experts. That may be the best place of all. Bicycle-frame tubing is tricky stuff and joining it is a real specialty.
The mechanism for hardening aluminum is nothing like that for hardening ferrous materials, you're growing or regrowing a specific microstructure and the instructions for the specific alloy for achieving the specific hardness HAVE to be followed. You can't wing it on this stuff and get good results. Commercially, the whole welded structure would be stuck in an oven and run through a specified heating and cooling cycle, time vs. temp. This speeds up the natural growth of the microstructure, which would normally take weeks or months at room temperature. One reason that adhesives are popular for joining heat-treated alloy pieces, no post-heat treat needed. When we were running motor home chassis extrusions, they'd be in the oven for a couple of days.
it's not just the temper, or lack thereof, that results from welding, but the structural considerations also. "retrofitted" frames are often seen to bend because the stay to which the tab is welded is not strong enough for the resultant bending force of the disk brake.
in view of both the welding temper and the bending, i say it's simply not worth trying this experiment. simply spend $99 on a new frame that's designed for the job from the outset and be done.