Yes, it's not always hcg that causes nausea the progesterone does too. I'm quite progesterone sensitive so I always get symptoms from very early on when pregnant as progesterone is higher than it would be if no conception occurred.
I've had bouts of bad nausea the day I tested positive as well as sore nipples and breathlessness/dizziness and frequent urination before a chemical.
I've had three, this current one being my third (almost in a row, just one no bfp cycle between 1st and 2nd).
1st was the classic chemical you hear about most often. Positive test that got significantly lighter 2 days later then bleeding started next day.
The 2nd one I got a faint positive then started bleeding the day my period would usually be (12dpo), the tests actually got darker until after day 3 of the bleeding when it turned from heavy to spotting, then they went negative.
This one is very much like the last one, I had nausea and sore nipples and breathlessness/hot flashes for a couple of days, then got a faint positive and started bleeding on Thursday evening (11dpo) it went heavy within 24 hours and has now gone to very very light spotting since this morning but tests are now negative.
So yes, you can have symptoms from the progesterone or from hcg if you test positive. Your symptoms may not fade immediately if bleeding starts and it's a chemical, it depends on what which hormone was causing the symptoms. Progesterone will drop before hcg usually, so my symptoms greatly reduced or disappeared before the test went negative as they were mostly progesterone caused.