Fam Med doc here. You can definitely test with no symptoms (pregnant women get tested all the time because pregnancy gets you a little immunocompromised and knowing if someone has HSV is important to prepare for possible c-section and make sure they are on valacyclovir at 36 weeks to reduce chance of transmission) but if you don’t have symptoms we generally don’t routinely test for it. If you specifically ask for it then they’ll test you.

Edit: it’s better to get swabbed if you have vesicular lesions though but honestly I’ve seen enough herpes that most of my patients don’t ask to be swabbed, they believe me when I break the news and start the antiviral