To my knolwedge, no entrance to Mem Drive is signed as a limited access highway. Per state law, that's bike accessible, see MGL chapter 85 section 11B, first paragraph: https://www.mass.gov/info-details/mass-general-laws-c85-ss-11b

That said, it definitely shouldn't be encouraged or suggested by routing apps in most cases. bicycle=discouraged might be the more precise value to use, since access denotes the legal right of way