I hope so because I have had 4 first dates in one week a few different times. That happened when I was doing online dating in 2007 and 2008. What would be wrong about it? You have no commitment to anyone at that point.
Yes it's completely okay. It's not like you're cheating on them, that is only a problem when you have become exclusive with someone. You have the right to look around and date as you please until you decide on who you want to continue dating.
If they're all first dates and none of them know each other, then you're not committed yet, but doing it all in the same week seems a little off. Generally I already know who I like before I ask for a date and only go for her until it either succeeds or she turns me down.