yes, remove the weak shit .. i agree with the other post, unless those side shoots are near the top coming from a cola or an upper branch getting good direct light , remove all that skinny weak growth near the bottom of the plant
you only need keep the most lush healthy/thick branches to produce a consistent yield of colas .. i remove branches/leaves to shape the overall canopy to allow even light and air distribution .. my plants grow pretty big so i often have nothing at all for the bottom 6 inch/1ft all growth removed, to only allow bud growth at the top of the canopy where the most intense light is
i call those types of shoots/branches "side shoots" its lateral branching something like that ..
some plants have the tendency to grow many long side shoots from each branch, ive found this a good trait as all these plants produced many buds sites all over the plants and were high yields, these multi side shoot plants are great for scog .. cant say i have ever thought of topping a side shoot though