Dissolve Polys Across Road

I have looked in the forums, but there is nothing that addresses my situation specifically.

I am dissolving polys based on common attributes, but there are roads within the resulting polys. The roads do NOT have the attribute that I am dissolving by and causes 'islands' within the overall dissolve. The obvious answer is to attribute the roads, which would take far too much time.

Is there a way to incorporate the roads in to the resultant polys without being attributed?

As always, thank you in advance for any advice!!