Well, I played it on a Windows 7 (64 bit) system on my old laptop, but not for long since I installed XP on it (being that it was an older laptop and didn't run very smooth in general).
So it should work... At least, it did with me.
My Computer
At a glance
Windows 7 Ultimate x64Intel i3-380M3 GB DDR3Intel HD Graphics 3000
It completely depends on your system specs, if they are good enough to run Sims you can run it on a 64-bit system. But when you first play it I recommend you run it in compatibility mode just in case it crashes some time.
My Computer
At a glance
Windows 7 Professional 32-bit (6.1, Build 7600)4096MB RAMRadeon ATI HD4870
I don't think hardware is going to be a problem with Sims 1. The game itself has lower requirements than Windows 7, so if the guy can run Windows 7 with ease in the first place he will most likely have enough machine to run the game too.
I would not run in any compatibility mode unless I know it's 100% needed or have a strong reason to do so. Just my opinion. I like to run things in the most "natural" way as possible.
My Computer
At a glance
Windows 7 Ultimate x64Intel Core i7-740QM8 GB DDR3NVIDIA GeForce 330GT
Computer type
Laptop
Computer Manufacturer/Model Number
Toshiba Sattelite A665-S6092
OS
Windows 7 Ultimate x64
CPU
Intel Core i7-740QM
Memory
8 GB DDR3
Graphics Card(s)
NVIDIA GeForce 330GT
Screen Resolution
1366x768
Hard Drives
Samsung 840 SSD 500GB
1TB USB3 external HD
Cooling
Coolermaster Notepal U3 notebook cooling pad
Internet Speed
3mbps ASDL
Antivirus
ClamWin 0.98.7
Browser
Opera 12.17 x86 (main), Firefox 38 (sec), IE11 (last resort)