I think it’s possible. Of course it is not straightforward and you can use now/log time (.ts) formatted to day only and select only logs, which have logday=today.
Idea (not copy&paste solution) - fix any functional/syntax issues:
count(
rate(
{<selector>}
| label_format today=`{{ date "2006-01-02" now }}`
| label_format logday=`{{ date "2006-01-02" .ts }}`
| label_format match=`{{ eq .today .logday }}`
| match = `true` [$__auto]
)
)