Yes
If you have Tinycore installed, open the appbrowser, and you can install GCompris and Lazarus. You need to be connected to the internet to download them. You can then copy them to other computers if you want.
Tinycore is ideal, as you can install only those apps you want on low performance computers. Tinycore is also much less likely to become corrupted than other operating systems.
If you want other apps which are not already available, you can either make them and submit them to the team, or request someone else to make them.