I wish to know if it is possible to have Tor Browser use my relay for traffic instead of its own client on start up.

At the moment if you change the proxy settings to your relay after startup 1) an observer would of noticed the specific Tor Browser traffic AND the relay 2) Tor Browser checks settings upon startup and if the proxy server setting is changed (eg 127.0.0.1:9050 instead of 127.0.0.1:9150) then it will refuse to start up. This isnt necessary a problem as you can just re-install / re-extract the bundle but upon start up you are still left with the default setting / specific Tor Browser traffic again.

I am aware extra bytes will show up on relay search, is this better than not using Tor for my use at all?

Thanks.