Depending on the pipeline you use and the compute resources available you could have a full workflow done in anywhere from several hours to a couple days. Illumina BaseSpace is free (for now) and has some example data sets with a bunch of canned pipelines for analysis if you're interested in trying it for yourself. https://basespace.illumina.com/
With particular hardware and software you can. Edico Dragen claims speeds for bcl -> vcf of 20 minutes [1]. With Microsoft Research's snap aligner and 450GB of memory you can get whole genome alignment in ~30 minutes and then variant calling can be done in a couple hours.
I've seen 200GB runs take 4 days, I've seen runs take 3 hours. Depends on your computing structure but more importantly is your IO. High CPU core counts and high speed storage access make a big difference, as does distributing the computational workload.