When using backtics to execute a command will variables be substituted correctly if placed within?

Yes, backticks (qx) will interpolate variable values. As Corion said, refer to perlop.

$result = 'somecommand $filename';
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Will the variable filename have it value substituted in or will it get interpreted literally as $filename?

You used single quotes (q) in your example, not backticks. So, your question does not seem to match your example code. Since single quotes do not interpolate, $result will contain the literal string $filename, which you can easily prove to yourself by using print to inspect its value, as Corion also pointed out. You probably want:

$result = `somecommand $filename`;
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or:

$result = qx(somecommand $filename);
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