I'm studying a species where there is a reference genome that is assembled *only* at the scaffold level ("unplaced scaffolds"). See here https://www.ncbi.nlm.nih.gov/genome/annotation_euk/Geospiza_fortis/101/. 

My question is 

 - Do people generally treat a reference genome at the scaffold level as
   if each scaffold would be a chromosome? 
 - Should a scaffold vs
   chromosome level reference genome be treated differently? 
 - What are
   the main challenges for using a reference genome that is only at the
   scaffold level?

Basically, I often read in population genetics textbook that we have to study "chromosome". But I have a hard imagine, when having only scaffold, how the theory applies differently.
All bioinformatic applications, including mapping (to a FASTA), will proceed as usual. For annotation, you'll also be fine as long as the contig/scaffold names are the same as the annotation file you're using. This isn't a major problem - the human reference, for example, has a number of unlocalized scaffolds and patch scaffolds that are relevant for annotation but aren't in the set of more thoroughly characterized chromosomes. Contigs/scaffolds/chromosomes are often treated the same by most applications.

So, to answer your questions:

 1. More-or-less. 
 2. Not really, but realize that your analysis may be impacted if all the scaffolds can't be localized to true chromosomes (e.g., are two scaffolds in LD because they're next to each other in reality?).
 3. Outlined above, but they're generally captured under issues resulting from 'assembly uncertainty' sensu lato.