In 2010 I trapped a Garden Warbler in Blaavand on April 29, even though the spring was cold and dominated by northwesterlies. So of course it is possible, but as with any unexpected record these birds ought to be carefully checked before they are reported.
Today I spend some hours in Amager Fælled looking for Sylvia warblers, especially for Garden Warblers. I looked through quite a few odd-singing Blackcaps to be sure, and they all proved to be Blackcaps. Whitethroats and Lesser Whitethroats were singing lively.
No Garden Warblers for me so far this year...
If you want to explore to differences in the song of these to Sylvia warblers, check this out.