NNC0, to make things simple, the answer to your question is a big NO.
The TCAS is not designed for that and the purpose of the display is not to show the accurate position of targets (other a/c).
It is forbiden to maneuver the a/c to avoid other traffic (as shown on the TCAS) display, in the absence of a TCAS RA (resolution advisory).
It helps indeed for situational awareness, but under no circumstances it should be a tool for the pilot to take the role of the atc controller.