Can a non-IFR rated pilot accept an IFR clearance, provided the operation occurs in VMC only?
Operating as PIC under IFR always requires an instrument rating and currency, regardless of flight conditions.
14 CFR 61.3(e) requires the rating, and there's no exception for VFR conditions:

(e) Instrument rating. No person may act as pilot in command of a
civil aircraft under IFR or in weather conditions less than the
minimums prescribed for VFR flight unless that person holds:
(1) The appropriate aircraft category, class, type (if required), and
instrument rating on that person's pilot certificate for any airplane,
helicopter, or powered-lift being flown;

61.57(c) requires instrument currency, again regardless of flight conditions:

(c) Instrument experience. Except as provided in paragraph (e) of this
section, a person may act as pilot in command under IFR or weather
conditions less than the minimums prescribed for VFR only if:

See this question for more details on filing IFR flight plans without being instrument rated (not a good idea).
Michael Hall suggested in a comment that some pilots might think that to operate under IFR they only need to file a flight plan and get a clearance, because of the wording in 91.173:

No person may operate an aircraft in controlled airspace under IFR
unless that person has—
(a) Filed an IFR flight plan; and
(b) Received an appropriate ATC clearance.

However, 91.173 doesn't override or invalidate any other regulation. The general rule is that regulations add up and you have to follow all of them unless the wording makes it clear that something doesn't apply (e.g. 91.1(e) says that part 91 regulations don't apply to part 103 ultralights).