Short answer, no.
Long answer you would need a way to get photos from the camera to a pc/mac then upload them to your server. I've worked for events companies in the past where we had to wirelessly transfer up to 4000 images a day over a distance of about 1/4 mile (driving experiences). We used WFT grips on canon bodies which were connected to an access point mast which was then hooked to a server which pulled the files from the camera, through the server and then onto 3 PC's for customers to view. They were then sorted into time/customer number order by a bit of software the company built.
If you can get your files from camera to pc you then need to look into the automation side of FTP transfer to your server but file size etc needs to be considered.
What's the need to have them displayed straight onto a website by the way?