Is a conduit required or recommended when running SER wire in unfinished space?
No, conduit is not required  

Wires equal to or greater than two #6 AWG or three #8 AWG can in fact be secured to the bottom of the floor joists per Code. 

334.15 Exposed Work
(C) In Unfinished Basements and Crawl Spaces. Where cable is run at angles with joists in unfinished basements and crawl spaces, it shall be permissible to secure cables not smaller than two #6 AWG or three #8 AWG conductors directly to the lower edges of the joists.

Technically SE cable ran indoors is treated as NM cable....

338.10 Uses Permitted 
(B) Branch Circuits or Feeders.
(4) Installation Methods for Branch Circuits and Feeders. 
(a) Interior Installations. 
In addition to the provisions of this article, Type SE service-entrance cable used for interior wiring shall comply with the installation requirements of Part II of Article 334, excluding 334.80

I'd recommend metallic flex though if a conduit is to be used.