Yes it is possible. As long as you have a Mac that does work and a USB media drive, that not currently of high importance, that contains 8 GB or more of free storage.
First you'll need to download a copy of the OS (El Capitan), you'll do this be going into the Mac App Store and finding it in the purchased tab. If it's not in the purchased tab, then you may need to end up download macOS Sierra (my condolences if you do).
You would also want to format your USB (of 8GB or more) in Disk Utility to Mac OS Extended (Journaled) under the GUID Partition Table.
Once you have the USB erased and El Capitan downloaded, you can install it to the USB drive. You can do this either using DiskMaker X 5 or Terminal. For when using Terminal you could watch this video the video shows you how to use the createinstallmedia tool for macOS Sierra, however Mac OS X El Capitan has the exact same Install tool, so the process of creating the terminal command would be exactly the same as long as the createinstallmedia tool is the same, which it is.
Once you have eventually created your Mac OS X recovery USB, you can then boot to it by holding shift ‘option’ turning the machine on to reach the boot menu, where you can select the Mac OS X recovery USB you have created once it is inserted into the device.
Also, before you do anything, or at least whilst you're waiting for OS to download, I recommend you go through the following guides (you need to do a web search for them since I can't reputation to just link them here):
Mashable - How to do a clean install of OS X El Capitan
Lifewire - Perform a Clean Install of OS X El Capitan on Your Mac
95to5Mac - How-To: Create a macOS Sierra USB Install Disk (same video I linked to earlier)