Short Answer: Yes.
F-1 students with pending STEM OPT application can also apply for F-1 Visa.
Such situation arises, if the initial F-1 Visa was issued with a validity of 2 years or the student maybe studying for more than 5 year (typical duration of F1 visa stamp validity).
It is also possible to apply for a new F-1 visa during this time. The Foreign Affairs Manual, which instructs U.S. Department of State officials regarding visa issuance, states at 9 FAM 402.5-5(N)(6)(e)
“As the STEM OPT extension is automatic for the first 180 days following regular post-completion OPT (when the student has properly filed Form I-765), the student may not necessarily have a renewed EAD. Therefore, any students having automatically authorized employment through the OPT extension may not be able to present a valid EAD when they apply to renew their visa. However, F-1 students in this situation can request an updated I-20 from the DSO, annotated for the STEM OPT extension, as well as proof that the I-765 petition was filed in a timely manner. You must confirm that the student’s electronic SEVIS record contains the same information as the updated hard copy Form I-20 before issuing a visa.”
Before leaving the country, please sure to ask yourself the questions listed at Can I travel outside USA on STEM OPT?