If you use the correct torx size and have the tool at the correct angle then damage should not happen, however, if it does then some suggestions here:
https://www.google.co.uk/search?ei=xiR3W5SbKOWdgAbQ3KLIBg&q=removing+damaged+torx+screw&oq=removing+damaged+rorx&gs_l=psy-ab.1.0.0i13k1.40761.54708.0.56786.32.32.0.0.0.0.197.3086.25j7.32.0..2..0...1.1.64.psy-ab..0.31.3005...0j0i22i30k1j0i67k1j0i131k1j0i3k1j33i160k1.0.7fW2kqQADb0
Yeah, the old plastic ones are now obsolete and been replaced with an upgraded option.
I have these in stock or you can get them from your local Nissan dealership which will save you on shipping cost.
Providing your hydraulics are good and your clutch is clearing and you are not to quick on your gearchange then the issue will probably be the synchromesh.
So the answer to your question is No, but the gearbox will have to be removed and stripped to fix the issue.
As what Jack has said, ^^^^ sounds like the beginning of PAS pump failure.
Low mileage pre-owned pumps are in stock depending on what model of 350 you have.
Just drop me a PM if I can help further.