Is there a way to access the full list of results in a Solr search page?
Yes and no. In any sane situation, it is the solr server that is handling the pagination. In essence, the server receives parameters, rows and start that tell it which "page" it will send. 

You could write custom code that would get you all the rows but that would require at keast one more query to the solr server. The first query (the default one) would find out how many results there are in total; the second one would fetch the whole set, setting rows to the total amount and start to 0.