I've been routed over odd surfaces a couple of times, but nothing a touring bike can't handle, and only for short (pushable) distances - not that I have pushed, and some of those were on NCN route 1 anyway! One reason is that c.t takes account of the surface information that is within the OSM maps, and that is sometimes erroneous. I have edited that data in OSM when I've found mistakes.
For the OP in particular, c.t shows unpaved sections in green on the PC screen, so you can see what it's doing. Also, if you left click on the route, a popup appears that gives you the option to view in google streetview. The unpaved sections won't have streetview images, but it's often possible to look at the ends, or if the unpaved section has road access along its length, such as a bridge or crossroads, it's possible to get a view,
I planned and rode lejog on cycle.travel. I forced it to route me via my home and the in-laws home plus some other personal preferences, then carved it up into dayride length sections and popped them all into the Garmin. I also took paper printouts using the pdf option, by way of backup. Never needed them though.
Edited to add, the hyperlink from the word Garm*n wasn't put in by me and I don't know how to get rid of it.