No, a modification made through an API call by will not log an interaction automatically on the constituent record and there is not an SDP (Site Data Parameter) or otherwise that can be configured in Luminate Online to log API modifications.  However, it is possible by submitting a separate API call, "logInteraction", to accomplish this. This would not be specifically tied to that API modification, but text could be manually input to note what the API modification was. Here is a direct link to that call on open.convio.com for reference:

http://open.convio.com/api/#constituent_api.logInteraction_method.html