Yes. LAS is probably the airport I've visited the most, and I've never been asked any questions when I go through T1 for T3 departing flights and vice versa.

PS - T1 has Clear, but T3 (E gates) doesn't, or I couldn't find it. While most of my flights depart from either D or T3, I always request to be dropped off at T1 for Clear, and then just head to D for the Amex lounge.