Interesting Project ! The complete battery pack charges to a bit over 116 volts. Your plan should work but you won't have any BMS functions except possibly balancing in the individual battery modules. The modules have electronics inside which communicate to the BMS module through the communication cables that connect all the modules. You probably would want some easy way to check the voltages of the 7 individual battery modules. Make SURE that the bikes battery pack and the extra pack are within a volt of each other or you could have a large inrush current from the more highly charged pack into the lower charged pack. I have burned my fingerers, flashed my eyes and vaporized a couple of 50 amp Anderson connectors by forgetting to do this once. Oh, and molten metal sprays out!
If the extra pack is wired in Parallel with the main pack it will charge with the main pack. There are a few buts of course. There will be no BMS function while charging or discharging and even though you can read the module voltage of each of the 7 modules there will be no way to measure the 4 individual cell groups inside each module but they should stay balanced for a long time and the balancers inside might work even though the internal electronics are not powered up. There is a green led on the top of each battery that flashes when the bike is either turned on, charging, or when the key is in the park position. I have always assumed that they mean the BMS and battery modules are on and communicating. That is not going to happen without the BMS hooked up. All that said, I run My Vectrix without a BMS and have ridden 4000 miles that way and the Chevy Volt cells I installed are still well balanced. You have to check them once in a while to be sure. Hope this helps.