After short investigation I found that it is possible, but it is not programmatically enabled by default.
Take a look in this file from app/code/core/Mage/Core/etc/system.xml:
// around line 1092 - magento v1.6.2.0
<use_store translate="label">
<label>Add Store Code to Urls</label>
<frontend_type>select</frontend_type>
<source_model>adminhtml/system_config_source_yesno</source_model>
<backend_model>adminhtml/system_config_backend_store</backend_model>
<sort_order>10</sort_order>
<show_in_default>1</show_in_default>
<show_in_website>0</show_in_website>
<show_in_store>0</show_in_store>
</use_store>
This three lines indicates configuration visibility in current scope
<show_in_default>1</show_in_default>
<show_in_website>0</show_in_website>
<show_in_store>0</show_in_store>
Unfortunately you cannot simply change those values to 1, because magento after upgrade overwrites all core files from app/core and you will lose all setup that was done there.
You can override config by overriding module system. Check: How to override a Magento administration panel?
I am a new with Magento world. Perhaps there's an easier way to do it
Greetings
Marcin