Yes. Copper bisglycinate can be taken at any time of day, including evening or bedtime. There is no evidence that it disrupts sleep or has stimulating effects. The only timing consideration is to avoid taking it simultaneously with high-dose zinc or iron supplements, which compete with copper for absorption.
Some people prefer to take copper at night because they already take zinc in the morning (or vice versa) and want to separate the two by as many hours as possible. This is a sensible strategy. The metallothionein-mediated competition between copper and zinc occurs at the intestinal lining at the time of absorption, so separating the doses by half a day effectively avoids it.
There is no established effect of copper supplementation on sleep at typical doses. Copper does participate in neurotransmitter synthesis — dopamine β-hydroxylase, which converts dopamine to norepinephrine, is copper-dependent — but the contribution of a single 2 mg supplemental dose to overall neurotransmitter dynamics is unlikely to be sleep-disrupting.