Yes, that's possible using CB Core Fields Ajax then by rendering the formatted HTML output of a field via a substitution. Example substitution as follows.
[cb:userfield field="FIELD_NAME" formatting="span" /]
For it to be properly styled with CBs CSS you'll need to surround it with CBs CSS namespace. Example as follows.
Code:
<span class="cb_template">[cb:userfield field="FIELD_NAME" formatting="span" /]</span>
There's nothing more to it beyond ensuring the field has ajax editing enabled in CB Core Fields Ajax. This can be used anywhere CB substitutions are supported. So for example in a Joomla article using CB Content Bot or in CB Content Module.