Will Search Engine crawlers follow the text URL with no "a href" tag?
At least Google occasionally does, especially if that would lead to an up-to-now unknown to them link.
They would store and crawl the URL, aye. They also usually do not account it as a part of the Link Graph.
Yeah, they definitely crawl all URLs that they find. That doesn`t mean that PageRank is passed, though.
Well...even if it doesn`t pass pagerank which is getting less and less important, it increases the visibility and helps in building the authority.