Is it a good idea to offer a less featured version of your software as open source as a marketing strategy? It obviously has worked well for companies like MySQL and wondering if it could work for small SaaS business apps as well.
Not really, unless the open source version of your product is compelling enough to attract a community of users. Many people make the mistake of posting their source on GitHub, expecting other people to show up. They usually don't.
One way to test your idea (of open sourcing your code) is to ask that question on a forum where your potential users are. If you receive a very strong response, then consider it. Be aware that it would take a really strong response to be a sign that a community may form. Posting a message on a forum saying "great idea, I'll definitely use it" is much easier than actually forking the code, understanding the code base and starting to do something with it.
I've seen good success will small free tools that 'Upsell' into a more feature rich product. When I was at NetIQ, we had several: QCheck, ADCheck, SQLCheck
Here's a link to SQLCheck (it was sold and updated to Idera): https://www.idera.com/productssolutions/freetools/sqlcheck
The key was that the free tool had to actually be useful and not be just a demo version of the real version.