It should be possible to use Page index in this scenario. I would recommend to double check the search settings of your page type in Page types -> edit your page type -> Search fields section. Is the custom filed marked as content?
As for the page crawler, yes it is possible to exclude certain elements on page, so they will not be processed by search crawler. Please check the following knowledge base article for more information http://devnet.kentico.com/articles/exclude-certain-elements-from-smart-search-index