Of Course you can!
All kinds of Recognition in your company are published on the Activities page, on the Homepage. And it's not just Recognition but Discussions, Events, Announcements etc. all kinds of activities are published on the Activities page.
If you want to view just recognition of other employees, click on 'All' on the top right hand side of the activities list:
Select Recognition or Team Awards and then your activities page is filtered for all recognition in your company only. Similarly, you can filter activities basis Announcements, Campaigns, Events etc. as shown in the image above.
Another filter which is available on the Activities page is on the top left hand side called 'All Activities':
This is a company hierarchical filter whereby you can filter the activities basis your team, department, city etc. For Example: I want to see who have been recognized in my team? For this, I filter 'Recognition' and 'My team' and I get the result. Simple!