That's not how it works. If you are operating OEI, the TCAS on the intruder will issue an RA, while you do not "cooperate" in the maneuver. If the intruder flies the RA and do nothing, no collision.
To my understanding that will only be the case AFTER you have selected TA Only.
If I am correct I have always thought it an unnecessary delay in the Engine Failure QRH that TA Only is No. 9 in actions. Any time you have a wounded bird I want to tell all over a/c around me that I can not necessarily respond to an RA. Some QRH's have TA Only much earlier. Why the delay with an engine shutdown? It takes 1 second.