Yes, it's just CSS and you can adjust it to whatever you want. On CB 1.9 you'll find such CSS at the below location of the default template.
components/com_comprofiler/plugin/templates/default/template.css
The below is the CSS for all the Connections menu link icons.
Code:
ul.cbMenuULlist li.cbMenu_UE_MENU_MANAGEMYCONNECTIONS a {background: url(/images/mini-icons/cbicons.png) repeat-y 0px -3000px; display:block;}
ul.cbMenuULlist li.cbMenu_UE_MENU_MANAGEMYCONNECTIONS a:hover {background:#dee1e3 url(images/mini-icons/cbicons.png) repeat-y 0px -3100px;}
ul.cbMenuULlist li.cbMenu_UE_ADDCONNECTIONREQUEST a {background:url(images/mini-icons/cbicons.png) repeat-y 0px -3200px; display:block;}
ul.cbMenuULlist li.cbMenu_UE_ADDCONNECTIONREQUEST a:hover {background:#dee1e3 url(images/mini-icons/cbicons.png) repeat-y 0px -3300px;}
ul.cbMenuULlist li.cbMenu_UE_ADDCONNECTION a {background:url(images/mini-icons/cbicons.png) repeat-y 0px -3200px; display:block;}
ul.cbMenuULlist li.cbMenu_UE_ADDCONNECTION a:hover {background:#dee1e3 url(images/mini-icons/cbicons.png) repeat-y 0px -3300px;}
ul.cbMenuULlist li.cbMenu_UE_REMOVECONNECTION a {background:url(images/mini-icons/cbicons.png) repeat-y 0px -3400px; display:block;}
ul.cbMenuULlist li.cbMenu_UE_REMOVECONNECTION a:hover {background:#dee1e3 url(images/mini-icons/cbicons.png) repeat-y 0px -3500px;}
ul.cbMenuULlist li.cbMenu_UE_REVOKECONNECTIONREQUEST a {background:url(images/mini-icons/cbicons.png) repeat-y 0px -3400px; display:block;}
ul.cbMenuULlist li.cbMenu_UE_REVOKECONNECTIONREQUEST a:hover {background:#dee1e3 url(images/mini-icons/cbicons.png) repeat-y 0px -3500px;}
You'll need to supply a custom background to your icon. It's best to make your changes and place them in the bottom of your Joomla template CSS file though as if you place in default CB template your changes will be lost on upgrade.