Hi,,, no, a cambelt won't affect 'balance' of an engine, as such. and if mis-timed, valve events and injection being off the mark would make an engine run very badly, not at all, or go BANG! If it is that a tensioner was not tensioning correctly, for some reason, it might be possible for symtoms like those mentioned to be apparent. The bike issue involves motors with camchains, not belts, but maybe the same kind of result could come about?
Think thus- an engine under full or increasing load and rpm, the belt would be pulled tight and under tension, decreasing rpm would leave it loose, but as no throttle input (foot off the gas) it might go un noticed. In the mid positon, as indicated, the belt might be neither loose nor tight, and able to let anything driven from it (cams, injector pump- but only a pressure issue as the injectors are time electronically of course) vary in speed related to the crankshaft, either up or down, sloppy if you will. That all said, there will be a crank AND a cam sensor, presumably and one or both wil set injection timing electronically, but if the belt is flapping the 2 sensor outputs to the ecu will vary and conflict, which may be what causes the fault. Imagine the belt as a piece of string,,, pulling = under good tension, push = not so,,, alternating between one state and the other - mayhem. Hope you get the ides, lol! And a fix!!