This really depends on the school(s) to which you are considering
application. Instead of asking others, make an appointment with someone in
the dental school's admissions office. Ask that person what that school is
looking for in an applicant. In other words get involved with the school to
which you hope to go rather than guessing what is on their mind.
Three major attributes needed by an applicant to dental school:
1. Academic ability - especially in the sciences
2. Manual dexterity
3. The proper psychological makeup. This will only be discovered by spending
a lot of time in a dentist's office observing the good and bad aspects of
dentistry. See how your personality matches up with needed by a successful
dentist.

Most applicants know themselves well enough regarding #1 and #2 above. Very
few have considered #3.

A Former Dean Of Dental Admissions

Entry qualifications for Cardiff (Wales, UK). Just need the equivalent of
A-Levels not a degree...
Scroll down..
http://coursefinder.cardiff.ac.uk/course_detail.shtml?course_id=15

Does it really matter what undergrad degree one has if
they think they may want to become a dentist?

Example.... could a person have an undergrad degree in
say engineering or computer science or accounting and
still become a dentist?