In a word, yes.
I did not want to spend my life configuring the new APP PART repository that is required to run APP PARTS from the Microsoft Sharepoint Store (which is new to Sharepoint 2013). So, I tried to add 2010 WebParts (and even one 2007 WebPart) and it worked for me.
THIS is a useful explaination of how to use STSADM to perform manual installs .
The three WebParts that I like the most (and are free) are:
Another great tool is the Sharepoint 2013 Glossary which you can find http://msdn.microsoft.com/en-us/library/gg191706.aspx