Siera on older (unsupported) Macs
Officially your Mac is not supported by macOS Sierra. However, for whatever reason, the option to upgrade to macOS Sierra is appearing in the App Store for a whole range of unsupported Macs. In fact, a few weeks back I saw this occur on a MacBook Pro (15" Late-2008) model that was running Snow Leopard 10.6.8, even though Apple doesn't officially support upgrading from this hardware or OS.

As to whether you can install it, the answer is yes, even though this isn't officially supported by Apple. If the App Store allows you to download the upgrade, then you could just download it (without installing it) and then make a copy of the installer. Once you've got a copy you could try installing from the original downloaded location to see what happens. 

If this doesn't work, the other option as you've already referenced, is to download the macOS Sierra Patcher Tool for Unsupported Macs. Make sure you read all the information on this page as it contains important information you should weigh up before proceeding. If it was me I would not proceed without a full backup ready so you could recover your system if all goes bad.

In the end, whether you should download the upgrade is up to you. Do you want macOS Sierra? Many of its new features are not supported even on Macs that are officially supported by the upgrade - so the answer to this will depend on what appeals to you in upgrading to macOS Sierra? To help you decide, go to Upgrade to macOS Sierra and scroll down to the Feature Requirements section.  

If what appeals to you isn't likely to work because it's only supported on much newer Mac models, then I wouldn't bother. This is especially so since you've already stated that El Capitan looks good on it.