Yes. Your squad avatar can be updated to an image of your logo.
Tap the top left navigation menu (hamburger menu).
Tap the three dots icon next to your logo on the top right, like shown below.
iPhone view iPad view
Upon clicking the 3 dots, the Squad selection menu will open. Find your Squad and tap the 'Settings' cog like shown below next to your Squad's name.
From there, tap on your Squad's current logo, or look for the pencil icon next to your logo like shown below and tap it. Additionally, this is also where you can leave a squad.
A menu will pop up, from there select from 'Photo Library' or 'Camera' options to update your Squad's logo. After selecting your image and cropping, just click on 'Use Image'.