It is technically possible to setup your own web server, and then you can have it use storage wherever you want. Though you would definitely run into problems like not enough upload bandwidth, your IP address changing and needing frequent updating (or using dyndns), or even violating your ISP TOS.
If you are asking if your website could somehow access your NAS, though, the answer, realistically, is no.
I'd argue that what you are paying for isn't so much "online storage"- you are paying for hosting, which is an altogether different ball of wax.
And, $99 a year for hosting isn't too bad. I pay about $450 a year (29.99 per month) for the hosting of mine, not including the cost of the two domains each year. (It is also a VPS, which means I get the joy of maintaining everything myself, or uh, not, as tends to be the case)