Short answer … yes.
When you install WordPress at the root of example.com you’ll be creating a third blog. Don’t worry too much about this, just recognize it’s there.
Create your network using subfolders for the different sites. Then create two new sites: blog and otherblog.
By default, any posts on these sites will use the URL structure: example.com/[sitename]/[permalink]
Then just import your old site into the new one and you’ll have the same URLs.
Unfortunately, there’s not really a way you can have the old one run simultaneously with the new one. All requests to the root (example.com) will be eaten by WordPress and redirected to the appropriate site. So if you set up blog first, any requests to example.com/otherblog will result in a 404 error until you set up and import that site as well.
If your sites were running on subdomains rather than in subfolders it would be possible … it’s an unfortunate circumstance many people who have shared hosting plans run into (and a good reason to upgrade your host).