Yes it can. Submillimeter telescopes are not limited to night time hours. Telescopes like the JCMT are mostly restricted by the amount of water vapour present in the atmosphere. This tends to be lower at night, and in the early morning, but can often (especially on sites like Mauna Kea) be low enough throughout the day to allow us to observe at any time. Scientific observations of planets and comets are the most common targets for daytime observing.
However usually the seeing becomes bad at submillimeter wavelengths during the day and pointing and focus observations become difficult after about 10am HST.