I have the HDD from an old laptop running Windows 7 Home 64-bit. I want to know if it's safe to boot into it from my desktop. I'm mostly concerned about driver issues.
No. It won't damage your system in any way, but Windows will be unusable.
boot in safe mode (f8), and wait untill windows start to recognize the hardware and installing the drivers that it has, then restart normally and see what other devices need drivers and proceed to install them.
most of the time you will experience lags and freezes,some programs will fail to load, windows will probably deactivate, etc... sometimes it just works well, is always best to reinstall the OS from scratch.
if you just want to get some files put it in slave and get ownership of the files (in case you used a password but the files are not encrypted )