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Yes

On one hand, it may be plausible that taking any measure that makes it harder to spread... favors a variant that can spread more easily.

On the other hand, spreading more easily means higher reproductive fitness under any circumstance. And not taking measures to reduce spread probably just means more infections faster, which is more opportunity for reproduction and mutation, which means you probably get higher fitness variations sooner.

Also I'm trying to think of anywhere in US/UK society for which "incessant lockdown" could possibly be an accurate description of policy much less behavior.

Imperial study was in the context of a tiered UK system that keeps schools, so increased infection from young people is my personal and ill-informed hypothesis of how the new variant achieved 50-70% increased r0 under restrictions.