Pushing too much spawn usually results in contamination; an MS syringe is mostly just water. Inside a bag extra moisture condensates which can help breed all kinds of things other than mycelium. All you need is one healthy spore to catch on, spread out, and stay clean to begin colonizing. So if an entire 10cc syringe was plunged into a single spawn bag then yes… that’s overkill. I doubt it will do much other than become contaminated. I would acquire more innoculant and try doing some brf cakes or agar to improve your technique and possibly even get to fruiting stage.