Is it possible for ccTLD and .com to both show for the same search?

I cannot find an answer for the life of me. My company is a well-established brand in the US and will be launching a storefront in the UK.

Let's say we own these two domains: xyzbrand.com (20+ years old) and xyzbrand.co.uk (brand new). Assuming it will take a few months for .co.uk to gain authority, should we expect some overlap on the SERP in the weeks following the domain launch?

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Ex 1.

London, UK user searches for "xyzbrand"

Results: ? ?

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Ex 2.

New York, USA user searches for "xyzbrand UK"

Results: ??