Can I use an acoustic bass for the course?

Yes you can definitely do this course on an acoustic bass guitar.

The main difference is that you won't be able to rest your thumb on the pickup when I tell you to.

Not having the pickup to rest your thumb is a bummer, but you can work around either by lightly resting it on the body of the bass, or resting it on the edge of the fingerboard, depending on what seems to work best on your instrument.

You can also look into installing a stick-on thumb rest on your bass, like this.