I think if you are coming from the engineering side, you might want to read up on sales. If the PM as mini-CEO of a product holds true where you work, the CEO mainly sets direction (for the product) and develops the business.
So sales (as in talking to customers) is really the part you may have less experience with. I think that exposure to real, imperfect, angry, complaining, confused, biased, excited customers is a good education in this. Your goal really is to interface the market/customers with the product/operations.
At first they put me to full time PM, then I wanted to get back to doing some code. I felt a bit lost as a full time PM at first, but after about 6 months, I'm getting used to it and suspect in the next year I'll be moving away from code as our product grows.
If you have the opportunity to do PM work in your current team, I highly recommend it.
So, would I hire a SE as a PM, I'd more likely hire the SE as a PE, or SE and try transitioning them if that is what they want. No guarantee they'd be good at it though.
Assuming you are in ENG today, can you take on some work from the PM team? The easiest way is to do this is in your own organization.
You can take the pragmatic marketing certificate, but it is kinda expensive. I would also read all of the free info on the web.
Good luck!