"Is it possible to conduct a bridge scour analysis with the use of unsteady flow data? "
1. Yes. It is not only possible it is probably preferable.
"I have only used HEC-RAS for steady flow modeling and I am unfamiliar with the options for unsteady flow."
2. HEC-RAS has many, many options for unsteady flow analysis. Read the documentation and work a couple of examples before you even try . If you have time and money, get some training from experienced users.
" I may soon receive input unsteady flow data."
3.Using your judgment, question the flow data and request more data when and if you feel you need to. Then. get the best "soils" data you can on the bed and bank materials.
4." Will I need to change this data to steady flow and if so can you offer any tips on completing this? "
See 1. above.
good luck