NASLite Network Attached Storage

I currently use NASLite on an older computer. If I get a newer computer that goes to sleep and can be wakened with Wake-on-LAN and then I install NASLite or NASLite+ should I expect it to go to sleep on its own and wake up when I try to access the NAS drive from another computer?

Thats not how wake-on-lan works. With wake-on-lan, you can boot a system remotely by sending a specially crafted "magic packet" to the cards Mac address. It won't just wake up because you try to access to host system.

Also the power management modes need support from the OS to operate, and NASLite doesn't have ACPI, or even APM. So, the computer wouldn't be going to sleep anyway.

What you could do, is set the bios to spin down the hard drives after a period of inactivity and disable to periodic smart checks in NASLite+. It wouldn't be a full power down, but your drives wouldn't be converting electricity into heat and noise when you're not home.