If you initially file in a country with a grace period after publication or public use of your invention, can you later secure patent protection in a country that does not have a grace period by filing a PCT application?

No.  Generally speaking, a PCT application is subject to the same national rules as a domestically filed patent application.  If the PCT application was accorded a priority date after a date of publication, that publication will bar you from receiving a patent in a country that does not recognize a grace period.

The results are similar with subsequently filed patent applications claiming priority via the Paris Convention.