Gaining

Is it possible? Yes, it is possible to consistently consume enough calories to add a couple pounds per day.
Is it a good idea? No. Gaining that much weight in a month is going to be hell on your joints not to mention your overall health. Generally the fastest sustainable rate is a pound per day. That still isn't great for you but there are examples of people who've kept it up for about 6 months without a feeder.

I've done 40 through sheer gluttony, I've known people who did up to 50 a month, it just isn't a sustainable rate. Depending on how you gain expect back and knee trouble. Also expect to feel really out of shape with gains that fast.

What was it like gaining that fast?

The gaining itself was awesome as most of it went to my belly. That said it also royally screwed up my back as well as making me feel really uncoordinated as my belly kept bumping things. Also had to learn how to move like a pregnant lady to compensate for my big ball belly since I'd had an apron belly before.

I wouldn't recommend doing that.
Even if it was possible to gain that much that fast there is so much damage it can do to your body gaining that quickly, like diabetes, and I forgot what they were called but they are basically like cysts and pockets in your fat it's really gross.
At most I would shoot for like 10lbs a month maybe 15lbs at the most but I wouldn't go above that.
Putting on a lot of weight really fast is a lot of stress on your body.