I want to be able to read content from the __DATA__ block in a file from within a BEGIN { } block [...]. Is this something that is possible?

No. BEGIN blocks are executed as soon as they are parsed, so the parser hasn't reached the __DATA__ token yet.

Here-docs might be a suitable replacement.

my $var = <<'__EOI__';
...
...
__EOI__
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I want to be able to read content from the __DATA__ block in a file from within [...] a packages 'import' function. Is this something that is possible?

No problem at all. The module's has been fully compiled (and executed) before anything can call its import, so it has no problem reading from its DATA handle.

---

Keep in mind that

use Gi::Testing::TestDB
    DataSource => [qw/DBI:mysql:database:address:3306 tester password/
+],
    Schema     => *main::DATA;
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is basically the same as

BEGIN {
    require Gi::Testing::TestDB;
    import  Gi::Testing::TestDB
        DataSource => [qw/DBI:mysql:database:address:3306 tester passw
+ord/],
        Schema     => *main::DATA;
}
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And thus the first answer applies.

Update: Added content after horizontal line.