The thing with recording is that you need <X> amount of throughput for <Y> amount of quality. You can think of it like filling your car with gas and going on trip. You need <X> litres of fuel to travel <Y> kilometres, having more gas won't make the trip faster so you shouldn't be worried about re-filling your tank at every service station you pass. You need enough fuel or disk throughput, maybe a little extra for emergencies, and after that you're not gaining anything at all. Likewise if you don't have enough fuel you don't finish your trip. Likewise you won't capture all the frames you're supposed to if you don't have enough HDD throughput.
Here's a chart showing the different popular recording software and their disk use per second. You probably care most about the second column. You can see that FRAPS will consume between 30 and 60 MB/s for 1080p30 video depending on what quality settings you use. As long as you have a drive that's capable of maintaining that performance you'll have no issues capturing things to it
How does the WD Green stack up?
They're fine, mostly.
You can see under the "best case" for streaming write they've got more than enough throughput (~110MB/s) to handle the demand. Unfortunately all spinning rust drives lose performance as they fill up so we also need to be concerned about worst-case performance too. The more full the drive, the worse it will perform. You can see in that review the WD Green drops as low as 53MB/s for streaming write. That's fast enough for lossy RGB 1080p30 FRAPS but probably not okay for higher quality/framerate options.
For the first half of the disk you should be pretty close to the "best case" performance, somewhere between 50% and 100% full you'll start to notice the performance fall off. As long as you keep the drive less than half full you'll have absolutely no issue using it as a capture device. In some cases you might even get as much as 75-80% full before performance waxes; it'll vary depending on the drive. On the other hand, if you intend to use the disk for storing data (old captures, documents, etc) then you probably want to consider a more capable drive.
The WD Black 4TB drive gives you a higher peak streaming performance (~150MB/s) which isn't that important for this use case, but it also stays above 80MB/s for worst-case streaming write. That means you'd have the option to capture 1080p60 with FRAPS using Lossless RGB if you wanted to, and even mostly full it's still going to provide enough throughput to avoid frame drops (the rest of your system might not, but it won't be the HDD holding you back).
You'll need to look up benchmarks for the same make/model/year as the disks you intend to use -- I provided examples for the current drives as a point of reference. If you're using an older model of the WD Black it's performance is going to be
worse than the new ones.