If one applied as a boarding student and received admission, would the student be able to transfer to a day student? Of course, assuming one reaches out to the admissions dept.
Only very rarely (from what we were told). If that is something you want you need to tell them ASAP.
Generally speaking, it would be pretty unlikely. The admission decisions were made based on each student’s application for day or boarding - these are different pools. Exceptions are sometimes made, and schools with different day/boarding balances may make those exceptions more often, but it’s almost never going to be as simple as “may I please switch?”
My guess is that all schools are different. At ds’s school, you can apply to switch from day to boarding once during your 4 years and then you can’t switch back. I know of a handful of day students who became boarding students. I don’t know of anyone who switched from boarding to day - not sure if that is an option.
I would think that if, the year you were accepted, you wanted to switch before the school year started “just because”, they probably wouldn’t let you. But if you had a valid reason, they might make an exception. Over the course of the years, you might be able to switch. If I go to BS, I’m going at least a year day, and then I might switch after we see how the situation is. Good luck! 
I have known kids who switched from day to boarding but only after being a day student for a year or two. Reasons were different but included family moving out of state, realizing that the distance to school was more challenging than anticipated, and realizing that they were at school all the time anyway so whatever upside they thought they’d have by living at home just wasn’t there.
This will vary from school to school, year by year, and by student. Schools want to fill classes but also fill beds… That means they can accommodate these requests only if there is a space for you in your new category and someone to take the spot you have vacated.
My son went to Lawrenceville. The switch (day > boarding) and vice versa is actually quite common. I know of about a dozen kids who did the switch.
I actually had to switch from day to boarding for one of my schools BEFORE THE DECISION this year because they told me I wouldn’t get in otherwise. I live 50 min away, so they thought I would drop out
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Agree that it is likely to be school specific. I know of a school that it is more competitive to get in as a day student than as a boarder, and the school said that because of this, they do not allow boarders to switch to become day students, but would allow day students to become boarders, if they had a bed available.
The policy is probably flexible depending on the year - for instance if the yield of boarders is high, the school may be happy to have the extra room. Worth asking! Good luck
Yes its true for many schools that day student pool is more competitive than the boarding pool. However I can imagine a few schools (Deerfield, Hotchkiss) where there are not many nearby day students.
I’d ask quick before revisits are done and folks send in their deposits. Still dont think it will be an easy switch. Many schools are oversubscribed these days.