Probably OK.
Depends how the old one is wired, and what the four Terminals are on the new one.
There may be small letters near the terminals i.e. "S" and "I", what are they?
I would say without looking at the relay, it will be one of two things.
1) The forth connection is in reality another set of contacts that is used to isolate the ignition system in the "START" mode only. If this is the case, this terminal will probably not be used in your application.
2) The fourth terminal is the "other" connection for the solenoid coil. Your current three wire job gets power for the coil from the BAT connection, you then supply a return (ground) on the "S" terminal to energize the coil. In this case, the fourth terminal would have a jumper wire going to the BAT terminal.
Waiter