No, it's not in the vein, technically, but that's how the cliché goes.
On the other hand, some amount of the injection escapes the muscle cells and gets into the blood and/or lymph.
“On the other hand, some amount of the injection escapes the muscle cells and gets into the blood and/or lymph.”
Of course. Oral and parenteral (such as IV, intramuscular, subcutaneous, intraoeritoneal etc...) drug delivery ultimately deliver the drug to blood and lymph.
This is how drugs get distributed throughout the body.