Hi there,
As long as when you assigned the program, you assigned it to all the clients at once, then yes!
Any update you make will immediately alter every program for all other clients assigned to it. A warning message will pop up after you save, letting you know that the program will be updated for ALL clients. Once you hit 'Okay' then your client's calendars will be updated.
Alternatively, if you assigned a group program and you only want to update it for 1 client in that group, you'll have to remove the program from that client and then assign them a new program.