In a word, "No". As Opus says, HSA contributions can be "employer" HSA contributions (even if you think you're making the deferral) or "personal" contributions (those you make directly to the HSA not through your employer).
The confusing thing is that these two types of contributions are treated quite differently. The "employer" contributions don't appear on your 1040 (but they do appear on form 8889) because this amount is removed from your Wages before your W-2 is even printed, while the personal contributions appear on line 13 of Schedule 1 (1040). They are also handled differently when an excess contribution is made, but I won't describe that unless you want me to.
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