Craft 3:
In Craft 3, a plugin can listen to the Element::EVENT_REGISTER_SEARCHABLE_ATTRIBUTES
event to modify the searchable attribute list of an element before it is indexed.
Craft 2:
Currently the answer is no.
Maybe it makes the case for some sort of onBeforeSearchIndex
event a plugin could listen to and influence what Craft adds to the search index, but given that manually updating the search index isn't meant to be a common occurrence (Craft keeps them up to date in normal element saving operations), I'd probably add the workflow you're using that requires frequent updates to the feature request.