Will upgrading ram help minecraft run faster?

Course it will.

Depends, what are ALL the specs of the computer?

Unlikely. Unless you're running at a really high resolution, or using wicked hi-res texture packs. @ 1080p I recall it only using 2-4gb @ close to max settings. The best way to speed up Minecraft is higher CPU clock speed.

Increasing the quantity will probably not help; Minecraft doesn't normally use that much RAM. Getting faster RAM with less latency may have some small improvement.

Up to 8GB of RAM, yes. After that no. I just installed a new AMD 2600 and that greatly increased the frame rate of my games where I can set all the bells and whistles and still have good frame rate. I play FTB Builder's Paradise right now and I'm getting 150 fps where Modded Minecraft is always more demanding than Vanilla Minecraft.