robots.txt isn't a requirement, indeed it's only voluntarily followed by spiders (as in they can choose to ignore it), so I think you'll be fine without it. The default is to 'allow all' and 'follow, index', so they should still be crawling the site correctly.

Check in Webmaster tools by fetching as Googlebot or alternative find a page and put cache:pageurl.html into google and see if it's cached it correctly.

That said returning a 500 instead of a 404 may be causing an issue that isn't obviously apparent and 500 is a bit too generic a message to say specifically what, but I would try and solve it as quick as possible. The benefits will depends on what you put in your robots.txt file