In general, no, but it’s actually slightly more nuanced than that.
First, you’d need to be a competitive applicants for JHU with all the necessary credentials, high GPA, high MCAt, outstanding LORs, interesting/unique ECs, a stellar research background. Assuming you’re equal to or better than most other applicants, the fact that your LORs come from a faculty member that the adcomm knows and respects might give you a slight edge for admission.
But that’s a whole lotta ifs and there’s no way to tell ahead of time if those will all fall into place.
IOW, don’t bet the bank on attending JHU undergrad giving you the necessary tip to get into JHU SOM.
Take a look at JHU SOM’s class profile:
http://www.hopkinsmedicine.org/som/admissions/md/students/class_statistics.html