My colleague, who works with this software, had the exact same question and it really bugged me that the answer was not readily available on the internet so I'll be posting this for posterity:
From the HaploView documentation under Haplotypes > Display
'View haplotypes for selected blocks by clicking on the "Haplotypes" tab or selecting "Haplotypes" from the Display menu. Haplotypes are estimated using an accelerated EM algorithm similar to the partition/ligation method described in Qin et al, 2002, Am J Hum Genet. This creates highly accurate population frequency estimates of the phased haplotypes based on the maximum likelihood as determined from the unphased input.'
So from this I gather that HaploView does in fact estimate phasing of unphased input data.
Disclaimer: I do not work with this software, nor is this my field of expertise.