Yes, and not automatically.
Back in the early 1990s, we were doing summed-price CBC at IntelliQuest. It was Jon Pinnell that showed me how to do it there. We added up the prices for the levels, and then randomly shocked the total prices by +/- a certain %. We estimated the utilities using aggregate logit under the old Systat program.
Nowadays, given that you can create "user-specified variables" within .cho and .csv files for submitting to our Latent Class and CBC/HB standalone programs, you can estimate the parameters within our systems.
Regarding the design of such experiments, conditional display can be used with a CBC attribute that provides discrete (rather than continuous) price shocks to do this. Then, you'll have the data processing work on the back end to formulate the "summed price" attribute in your customized .cho or .csv file.