Yes, you can sync data between multiple accounts.
Road Trip doesn't use iCloud for syncing data, so it does not matter whether two devices are using the same iCloud account or not.
If there are multiple Road Trip users who use their own Dropbox accounts, there are a couple of options available.
We recommend using the same Dropbox account when syncing multiple copies of Road Trip. Road Trip's Dropbox account settings are separate from the other apps on your iPhone, so you can use an auxilary Dropbox account with Road Trip while still using your primary Dropbox account with your other apps.
When you enable Dropbox in Road Trip, the Dropbox app will launch and ask you to authorize Road Trip. Select Use a different account and then sign into the Dropbox account you wish to use with Road Trip.
Dropbox allows you to share folders between multiple accounts. You can set up a shared Dropbox folder and then configure Road Trip to use this folder.
First, set up a shared folder in Dropbox. For instructions, visit the Dropbox website: How do I share folders with other people?
Next, configure Road Trip to use this shared folder. In Road Trip, select Sync and Backup -> Dropbox Settings -> Folder Name and enter the name of the shared folder in your Dropbox account.