Yes
If so, would such bursts cause skewing in results?
Yes. The Theory behind carbon-14 dating relies on a constant rate of upper atmosphere 14C generation, based on a constant flux of solar protons converting nitrogen-14 to carbon-14.
The Practice attempts to compensate for variations in proton flux by 14C dating samples of know ages and making a table of 14C dates Vs calendar dates.
This is further complicated by plants having species specific varying rates of 14C uptake.
The upshot?
Carbon-14 data provides a fairly accurate estimate of age, providing the sample isn't so old that all the 14C has decayed.
How does the existence of additional carbon-14 affect dating? Do objects absorb new amounts from the burst? Do objects with carbon-14 convert slower if atmosphere contains more carbon-14?
Wondering about the process.
I get the estimating is pretty accurate, but wonder about the variables. Do these known and unknown variables have a significant +- range that causes dating to be within decades/centuries etc as we go further back in time without less corresponding data points? Could local conditions have significantly different rates than the assumed average?
Or are these fluctuations minor compared to the totals?
Not sure why but I would guess that such bursts might have larger affect when recent that if long ago.