Dual Booting doesn't double requirements
Dual Booting does not mean Windows 7 minimum requirements + Ubuntu minimum requirements = system minimum requirements.
Dual Booting minimum requirements are about 15 GB partition for Ubuntu and common applications. On my 16.04 I give Ubuntu a 30 GB partition out of 880 GB available.
If a Windows version will run a similar Ubuntu version will run
Running Windows 7 with 2 GB ram will be sluggish at times when loading multiple modern web browser pages and videos. The same will happen with a Ubuntu version running similar applications.
As others have mentioned there are scaled down versions of Ubuntu with smaller RAM requirements (starting at about 512 MB I believe) and you would be well served to investigate these versions.
Modest performance improvements
The best improvements to speed you could make on your rig are:
- Upgrading RAM from 2 GB to 4 GB for about $100.
- Upgrading 300 GB HDD to 240 GB SSD for about $150.
Note that on some machines upgrading may not be possible depending on system maximum limits.