The short answer is YES. You should. But, it really depends on the context.
In this, I will assume that you know what a RAM stick is and its purpose in your system. And If you're not familiar with it, You can see for yourself.
Familiar with the concept of RAM? Alright, Let's talk about the topic at hand
You might be buying expensive RAMs with higher speeds for your gaming PC, 32Gigs, 64Gigs, or 128Gigs? Depending on your motherboard specifications. Or you will be buying ECC registered RAMs for your server or for your workstation. Either way, you will be investing a lot of money on this expensive hardware and if they fail in a production environment, the result can be pretty catastrophic. So it's always a good idea to test them before committing.
Ask yourselves these questions
Are you buying brand new RAM sticks? If the answer is yes, then it won't be necessary because you're covered with your warranty. And you can see if there's something wrong when you assemble your computer and finally POST it. Your BIOS lets you know the amount of RAM installed in your system. If everything checks out. Mostly, you're good to go. But if you have the time, test them. It might pay off.
Buying used hardware?
This is where it gets tricky.
Buying second-hand or used hardware. In this case your RAM. You don't know the history of the RAM stick you're buying and the miles it has on it. It's not like you can check if it's good just by looking at it. That's not the case here. So it's always a good idea to stress test it in this situation. Just simply ask the place you're buying it from that would it be okay If you stress test it. Trust me, it's worth the trouble.
If you get issues such as blue screen (BSOD), random system reboots, paging errors, caching issues, low read/write speed, and hardware glitches. Then, RAM Sticks will be a good place to start troubleshooting. It might be dust in your RAM ports or the stick might not be seated properly. It can be something as simple as that. But then again, it can be something pretty bad like a RAM stick with errors. You can make sure by testing it.
You will need the following:
Flash drive with at least a 4GB capacity. (To make it bootable)
And a small software called MemTest 86.
This is a free, stand-alone memory testing software for x86 and ARM computers with premium options available with more features for enterprise environments, but for this particular purpose, the free version is enough. I will link a video below to see how it is set up.