Pretty much anything is possible. Taking a look, when i hit the button, it brings up a Modal with this url:
http://kentico10.avastonetest.com/CMSFormControls/Selectors/InsertImageOrMedia/Header.aspx?output=url&pagetypes=All&attachments_hide=1&documentid=1202&parentid=198&content_site=BlankSite&content_userelativeurl=True&content_culture=en-US&editor_clientid=m_c_webPartProperties_form_LinkUrl_txtPath&siteid=2&hash=fe391d5043b1a893919f5c53fcec2cdc796222733dbd879a8f7adc1a21ce4bf1
After making a default selection of Media Libraries, i close, then re-open to a modal of this url
http://kentico10.avastonetest.com/CMSFormControls/Selectors/InsertImageOrMedia/Header.aspx?output=url&pagetypes=All&attachments_hide=1&documentid=1202&parentid=198&content_site=BlankSite&content_userelativeurl=True&content_culture=en-US&editor_clientid=m_c_webPartProperties_form_LinkUrl_txtPath&siteid=2&tab=libraries&hash=66c432b6e413594204f9d7b3bbcc5e234a99307aeec2a7d53faba0e2211e1a8e
Notice the tab and the hash are different.
The hash i believe is part of the Modal UI class, i looked into at one point, and i believe it's a hash of all the parameters for security purposes. You may be able to look into how it's calling the Modal and set the tab...but it will definitely be a challenge!