I think there is probably a better way—and I’d like to know one but don’t have time to code dive, play—but this kind of thing should work.

use warnings;
no warnings "uninitialized";
use strict;
use MyApp::Schema;

my $schema = MyApp::Schema->connect("dbi:SQLite::memory:");

my ( $first_source ) = $schema->sources;
my $ok = eval {
    $schema->resultset($first_source)->count || 1;
};

if ( $@ =~ /no such table/ )
{
    warn $@;
    print "Trying to deploy...\n";
    $schema->deploy;
    $schema->resultset($first_source)->count;
    print "Deploy seems good!\n";
}
elsif ( not $ok )
{
    die $@ || "Uh... something bad, something, something\n";
}
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