You really have to use the Modulus of Elasticity for Metals (amesweb.info) which is a measurement of how stiff a material is. This if factored with the shape. A hollow rod will be stiffer that a solid rod for the same material cross section area. Here is an online calculator for bending; Deflection calculation (converteraccessory.com) for a rod.Figure about 7" or so, I think. I was just comparing by bending a pieces of 1/4" and 3/8" that we had laying around the shop. The 3/8" thick aluminum all-thread was not hand bendable in a 2 foot long section.

Actually, I also looked up the tensile strength and sheer limit of both and took a WAG that the deflection would be comparable. The 1/4" SS 18-8 all thread has a TS of 70,000 psi to give a TS of the 1/4" rod of 2,520 and sheer of 1,580 using 60% (as a guess). The 3/4" 6061 all thread has a TS of 40,000 but the extra thickness gives a TS for this rod of 3,100 and a sheer of 1,860 using the same 60%. The 3/8" aluminum rod is about 23% stronger based on this math.

I am definitely not an engineer so I just looked up formulas and tensile strength area of threaded rods online (engineeringtoolbox.com and there were a couple of bolt mfgs that had the same formulas) and this seemed pretty accurate based on trying to hand bend the threads that I had at the shop. Let me know if these are wrong or if I'm going down the wrong hole.

But it looks like my first guess was wrong and the deflection of a 3/8" AL is about 1/2 of 1/4" SS for the same load. The moment of inertia for the larger diameter over rides the higher Mod of Elast.

This is not really a comment on whether the deflection of the 1/4" SS would be a problem, but if the 3/8 AL is at all questionable, the 1/4 SS would be a lot worse.