Welcome to the Forum. We're all a little crazy here, just some more than others.
Yes you can. But I think most people (at least here) have eased into the business. Where you at?
Disclaimer: This is my opinion. I don't need to saw to earn a living.
Some basics in starting any manufacturing business:
1. Identify your market. Who you gonna sell to and what are you going to sell. The more defined you can be the better chance of success. You can't compete with Lowe's, Home Depot or even the local lumber yard selling 2" x 4's to the home building industry. Just can't do it. Are you going to primarily cut hardwoods, soft woods, or both. Are you going to just saw boards as a service or sell your sawn lumber to the public?
2. Identify your source of raw materials. Where you going to get logs.
3. Try and find a niche that fits you and the area your in. Your area somewhat defines what your going to have available to cut. Some people specialize in selling wide boards or specialty cuts to high end housing (fire place mantels) or figured woods to hobbyist or long timbers, just custom sawing, etc, etc. Lots of niches. Some make their niche the only thing they do, other just lean strongly toward it. I know a fellow that the sawing is only used to feed his other business because he can't buy what he needs. Has to cut it himself. Another I know just cuts one kind of wood, Pacific Northwest black walnut. I think diversity is good, some don't.
4. Equipment (the saw) you buy should fit what your doing and you never have enough equipment. In general the more you spend on a saw the more capabilities it will have. But you may not need capability beyond a certain point. You can always upgrade saws if that would make you more money and that is what you want. Lots and lots of variables.
Try and find a local mentor that is willing to help you. Somebody that's basically doing what you want to do. Small saw millers, in general, love to help others with knowledge and share their experience. That's what this forum is all about.
Here's a link to a fellow that started in this business making fishing tackle boxes out of figured maple he bought at a local hardwood mill. He now does over $1,000,000 a year selling woods that he saws. The "Instrument Wood" is a new thrust in niche marketing, He imports a lot of his logs in containers.
http://www.cookwoods.com/ Usable saws start at around $5000 and go up (way up) from there. Low end would be a chain saw mill at around $2000.