Yes, you will be able to provide additional coverage. If you cannot hard-wire the second 3502i, you can run it in Mesh mode, which means it will wirelessly connect to the primary 3502i with one of its two radios, and duplicate your WLAN broadcast with the other for endpoint connections. In order to do that, you'll need to adopt the new 3502i into the Cisco Wireless LAN Controller software; then you can put it into Mesh mode and deploy it.
If most of that is confusing, I would highly recommend hiring the upgrade out to an IT firm with Cisco CCNA (or higher) certification to make sure the work is done properly.