Is SIM power required?

For our application we are not using a SIM card. Is there any reason
that SIM needs to be connected from the TPS65950 power chip to the
OMAP3530? I would like to remove the trace on my custom board but
don't know if it will have any ill effects.

I would connect it to keep the rail powered. It is called SIM but it drives several different pins that you may or may not be using. If you can verify that the pin powered by the rail are unused, you should be OK removing it.

Gerald