As you specifically state:
Would it be possible to systematically deduce what this organism looks like and behaves like without reference to anything else (ex: a repository of genomes of known living organisms)?
No, no chance at all, we certainly wouldn't even be able to determine a single gene function, other than that it codes for a series of amino-acids. After all, even simple genes of say 100 bases in DNA will still have 33 amino-acids, and most people don't remember that sort of information without cause, and the only way we can acquire that easily information is through repositories of information. The only way we could do something approaching working this out would be to take portions of the genome that we could identify as genes (start/stop codons), then express them one-by-one and empirically work out the function through classic biochemical methods. This is very laborious and time consuming - it would take many many person-hours per gene and a LOT of resources. However, this is how functions of novel genes and their related proteins were and still are worked out.
With reference - perhaps, at least partially. From the sequence and with access to a repository such as Genbank we could deduce which type of organism it was by comparing to known genomes from other organisms in a process known as phylogenetic analysis. You could certainly tell which of the kingdoms it came from. In each organism there are conserved bits of the DNA (or RNA) that tell you which groups they are. For example all DNA based bacteria and archaea (that I know of) you can use the 16S ribosomal RNA sequence, which will identify bacteria and archaea down to genus and species level.
For instance, you might have a genome that gives you information that it is a bacterium of the Staphylcoccus group, meaning that you can deduce that it is very very likely that it will be a small bacterium which is a round ball shape, and will stain positive with a Gram stain. You could also likely identify some genes and their function based on homology.
You can apply this process to other genomes, for instance a mammalian one will tell you that it had fur, produced milk, was warm blooded, quadruped, spinal column etc.