Can a 3G android phone support 4G? I own a Samsung galaxy note 3 N900 which is a 3G phone.

Its specification include 

HSPA+ : HSDPA 42.2 Mbps and HSUPA 5.76 Mbps

In my area, Airtel is providing 3G at the speed of 2 Mbps and 4G at the speed of 10 Mbps.

My phone does not support 4G but it does support 10 Mbps download speed.

Will that 10 Mbps 4G plan work on my phone or not?
your phone doesn't support 4G it supports 3G++ which almost 4g and supports high speed downloads , the short unswer to your question is you can't use the 4g plan proposed by your carrier due to your phone's hardware limitation.
the bright side is HSPA+ is not so bad you will not notice the difference.