Is it possible for a 2mm disc protrusion with annular tear to cause severe sciatica in entire leg?

Herniation with Tear. The disc is like a jelly filled donut. If the donut is compressed too much the jelly leaks out through a break in the donut's bread. The same is true with a disc, the tear is caused by the compression resulting in a herniation (protrusion) and the jelly (inside portion of the disc) is either leaking out or trying to get out. This can result in chemical inflammation of the nerves causing pain.
Yes size is not . Always important in terms of a disc herniation as it can be more of an inflammatory or chemical reaction leading to the pain rather than a direct compression or pinching of the nerve --sort of like having your hand near enough to a flame to burn but not in it. Sometimes, just an annular tear without the disc herniating through the annulus can provoke the sciatica.
Unlikely. It is thought that the annular tears may leak protiens that irritate the nerve root without compression i recommend confirming the suspected pain generator with a selective epidural injection. Can cause siatica back of leg at L5 or s1.What level was the protrusion at? By entire leg did you mean the front of the thigh as well?