Yes, you could run a weld bead on the back side, but I don't believe you need to.
I think it is instructive to remember a few things:
Silver bearing solder will bond dissimilar metals amazingly well, so rust and paint are the only things you need to remove in this case.
It applies at such a low temperature it won't deform nor warp thin metal and you can apply it with a handheld propane or MAPP torch.
It is easy as pie to use...once you get the hang of it, you'll be amazed.
If you make a mistake just heat it up, shake or brush the solder off and do it again. Heck, at that temperature I've even used a work glove to brush molten solder off.
It is stronger than a 99 cent Mexican plate lunch.
In the 60s, I took advanced level welding classes for 9 months and then worked as a specialty commercial welder until I realized how fast that work could turn a young man into an old man during the summer in Texas. The instructor had worked all over the world and had a very impressive knowledge about the subject not to overlook a doctorate in industrial arts. He was very big on using the right stuff for the job at hand...ie, not using a Howitzer to kill a rat. We spent weeks learning about solder...the myriad different types, all their properties, how to apply them correctly and all the benefits and advantages from using them. I've mentioned silver bearing solder on this forum numerous times, and usually I get the idea about 5 or 6 people around here have even heard of the stuff. My sincere suggestion (to everyone) would be to study and get familiar with it. With silver bearing solder you can join/repair mild steel, copper, brass, stainless and cast iron. A couple of years ago I even used it to repair a cracked carburetor float bowl with success. IMPORTANT NOTE: silver bearing solder is NOT the same as silver solder. Silver bearing solder is a non-lead solder with properties you won't find in any other non-lead bearing solder. Good luck.