Sort of. Sometimes.
Viruses evolve according to evolutionary pressures. I'm surprised we don't see Covid mutations that invalidate PCR tests - perhaps it's too soon, or even, who knows, maybe they are there and we don't know?
The common trope is that if the virus is too deadly, then it doesn't have a chance to find new hosts. This is kind-of what happened to "SARS-1" - it tended to kill its hosts before they could pass it on.
Unfortunately, this is only a weak effect in Covid. Most of the spread happens well before people are very ill; in terminal stages of severe Covid, many people in fact would test negative for virus presence. So there is little evolutionary pressure on the virus to be less deadly - by the time it kills people, we are spent vessels from its point of view.
I suppose a mutation that makes it completely benign would be beneficial, as current rules on self-isolation curb the spread of strains causing symptomatic disease.
There are pressures that make it more deadly: a mutation leading to higher viral load is both more deadly and more transmissible. So unless the transmissibility increases too much (and virus is way too deadly), we might even expect the virus to become more deadly. This hasn't happened yet, thankfully.
An example I used elsewhere was the introduction of Myxomatosis in Australia, to control the invasive rabbit population. Over time, the local strain evolved to be more deadly, but with a longer incubation periods. This way, bunnies had more time to pass the virus around, then once that job was done, the virus was happy to kill them off.
On the flipside (and very long timescales), since some people appear to be genetically more resistant to the virus, you can expect natural selection to do its job. But since overall death rate from Covid is low-ish (no more than 1%, you'd say, and skewed towards older, non-reproducing individuals) this would take a long time.
Another hope is that, if the disease is less serious in children, perhaps immunity it built up during the usual period of childhood infections. There is another coronavirus, which causes a mild cold in children, but can be very serious in adults (apologies, I can't remember what it's called). Thankfully, a single infection gives more-or-less complete lifetime protection - so most people have it as children and never worry about it again.
In either of these cases, we're talking about generational timescales.