Conceivably a lot - however, I wouldn't advise going overboard with HA filler. Men here, especially those without any work done, have no idea how significant 0.5"-1.0" is in actual Girth. The change in volume is quite significant.
If you want a natural end-result with HA, go with practical goals (like I said, try not to exceed 1 Inch in circumference). This not only will improve how it feels and looks, but will be much easier to manage if you need future Revision work.
To be honest, I think going overboard with any filler increases the risk for aesthetic irregularity. I think the "squishiness" effect is a bit overblown - your natural Erect penis still has some "give," much like why dildos are not rock hard like vibrators. Furthermore, overfilling is equally problematic for more permanent fillers like Ellanse or PMMA, where the skin can become "too rubbery" to the touch.
In other words, HA, Fat, Ellanse, Radiesse, Renuva, and PMMA are all viable fillers when (1) medical grade; (2) performed by a qualified & experienced practitioner; and (3) not over-filled, especially not all at once.
I also agree with Hyperbol - regardless of the contour/palpability of your penis, the vast majority of partners are going to dwell on how much it fills them up... if they've seen enough penises they'll know how much variation there is in size, shape, veins, coloration, etc. What COULD raise suspicion is if you over do it. Just like lips, you ever see a woman with disproportionally large lips? The ones who add just enough to plump them up get away just fine, same applies.
On a side note, if you have a significant other who's comfortable with your decision and aesthetics aren't high on your priority list, then sure, you can probably exceed 1 Inch, many have. Just be aware of your circumstances when making these decisions.