Are there any negative effects to go into "suspend mode" wile an application is in the middle of running?
No, an application should be able to cope with this just fine. If it doesn't, it would indicate a problem with the application.
An application doesn't even have to know it suspended, it may just notice the normal side-effects of associated things like active network connections being cut off.
An application like Transmission will notice that any network connections it had open suddenly close. It should just continue to try to open new connections, no harm done. This is just the same as if your internet connection went down temporarily.
An operation like cp or mv should be fine particularly if the operation is on local drives - it should continue after resuming, except in the case that the device it was copying from or to has been disconnected in the mean-time (or was a network device and the connection was lost), in which case it would issue an error message, just as if you had disconnected the device yourself while the computer was running.
So to summarise, suspending your computer usually won't harm the running applications any more than the network dropping connection, or changing the time on the clock, or disconnecting devices, might at any time. An application doesn't need to be specially programmed to be able to suspend and resume properly.