Unfortunately a majority of WiFi/Overall Phone Reception is relayed through that part. This part is called the "Antenna Bridge" or "Speaker Assembly" (both the same thing).
As you can see, there are 4 metal feet that connected to the iPhone frame. The feet then use the entire frame of the iPhone as an "extended antenna", and if broken off greatly reduce iPhone reception.
These feet are connected to the antenna cable which MUST be connected to the logic board or you will not receive and WiFi/Phone Reception at all.
So in short, if you do not have this part installed, you will not be able to make phone calls or connect to WiFi, disabling the "Phone" and "Internet" aspects of the iPhone. If you can survive without these functions then you can just use your iPhone as a music/gaming device, however it is not recommended to leave parts missing inside an iPhone on purpose, as it can possibly cause other parts to fall out of place and become damaged.
As a short term fix, you could possibly get some type of material (plastic or rubber) and cut them into the size that covers the two feet that connect the speaker to the logic board and place it between the feet to stop the connection from being made. Alternatively you could just break the feet off and render the entire part useless, however seeing as the part is damaged already and is in need for replacement it is also another viable option.
Hope this helps! :)