Definitely! The Liberty 404 is specifically designed to be used for a remote sink drain or a laundry application as long as the water temperature does not exceed 140 degrees Fahrenheit.
Per the product manual:
Provision is made for a vent stack to allow extra volume for high suds conditions, and to ensure proper drainage of the
fixture. HAND-TIGHTEN ONLY. DO NOT CAP-OFF VENT. DO NOT use ONE-WAY QUICK-VENTS or AIR ADMITTENCE
VALVES as they will not guarantee proper fixture performance. The vent pipe should have a union to facilitate removal if required
and shall be connected directly to a building or house vent.
You can also check out the complete manual HERE if you would like more information.