I do know that they'll grow larger and faster and outcompete the other chicks (brown headed cowbird chicks do not push other chicks out of the nest though), but it would still be cool to observe from a ornothological point of view, because I never have before.
On top of that,
here's an article by the Audubon society about why you shouldn't remove cowbird eggs from a nest.
"Itâs a natural process and we shouldnât attach human values about killing or being sneaky to the natural world."
Brown headed cowbirds are native here, so not only is it illegal to interfere with their eggs, it's also detrimental to their population.
"While permits for cowbird control are granted, itâs only done when theyâre considered a threat to endangered birds. For example, in Michigan, the U.S. Fish and Wildlife Service traps an average of 4,000 cowbirds every year to protect endangered Kirtlandâs Warblers."