I think you could get the OP’s idea to work, the flow of fluid would be limited by the smallest aperture in the system, so if you only just cracked the bleeder nipple on the caliper, you could limit it to a very low flow.
However, what’s the point. It’s just another way of feeding fluid into the system through the caliper. If your brakes are still spongy after bleeding, then you’re either not getting all the air out of the system or something else is flexing.
If you start by drawing some fluid out of the caliper and into the syringe, you can check that there are no air bubbles in the caliper. Then force all the fluid in the syringe through to the lever, use a container to catch the extra fluid that will come out of the lever. This will ensure that you have flushed all the old fluid out of the system along with any air bubbles in the hose.