Sure, but it would allow you to track the movement of your own antibodies over time.
So it could be fun, like some people track their weight over time, or blood pressure, or fitbit activity. But
@skyguy918 wondered "if there's some number that translates to an immunity threshold" and we seem to be far from knowing that. Two reasons: We don't know what level of antibodies allows re-infection (or if cases like that Nevada one are rare flukes). And we do know that even if antibodies become undetectable, there may well be memory B cells that are able to quickly ramp up antibody production if we're reinfected (at least this is true for some other diseases), as well as T cells that may prevent a second illness.
I found a couple of clinical trials that are trying to figure out this relationship between antibody level and immunity.
https://clinicaltrials.gov/ct2/show/NCT04540484?id=NCT04540484&draw=2&rank=1COVID-19 IgG Formation in Physicians at ALGH and Their Household Members"...To date, there have been no studies confirming that IgG antibody formation confers immunity, but studies are ongoing. Furthermore, data is lacking showing conclusive persistence of (possibly protective) antibodies over time." So they're studying physicians at a particular hospital in Illinois, where there are a lot of covid patients treated. The doctors' antibody level will be measured every 3 months, and they'll also be able to relate this to any covid (re)infections that develop in the doctors. That study is expected to take a year.
https://clinicaltrials.gov/ct2/show/NCT04411147?id=NCT04411147&draw=2&rank=1A Longitudinal Study of COVID-19 Sequelae and Immunity"Objective: To learn about any long-term medical problems that people who have recovered from COVID-19 might have, and whether they develop an immune response to SARS-CoV-2 that provides protection against reinfection." They'll assay antibody levels every 6 months, for 3 years. This one is recruiting 900 participants, and anyone who meets the criteria is welcome to apply. You get free antibody tests! I don't know if they reimburse you for transportation costs to the NIH lab in Bethesda MD, but you can use points and get an unusual TR out of it!