When your backup is running and encounters a file which is "open" (some other task is using the file), the backup software will typically do one of two things:
1) It will ignore the file, and the file will not be on your backup.
2) It will backup the file as well as it can. The file will be on your backup media, but some data may be bad (for example if a database process was in the process of updating an index when backup came through).
When you try to restore these files from your backup media, the associated programs may or may not be able (or willing) to correctly read the files. For example, with Oracle, there are multiple pieces of a database, and if the time stamps are not identical on all of them, the program claims that the database is corrupt and refuses to open it. Look for this and similar problems with Exchange and SQL server.
Office files present a different problem. Word, for example, makes a temporary file, and writes changes to the original file on close. Your backup will not save the changes. No backup software will really deal well with this -- your users need to not leave files open overnight.
Because of the possible consequences of not being able to recover database files, your backup software MUST be able to properly deal with these files. Many vendors of backup software have add-ons for various types of files to handle these problems. (Some of these actually log into the database and read record-by-record.) You must let your vendor know what types of packages you run, and you need assurance from your vendor that the files you have will be properly backed up.
Disaster recovery refers to how much work it takes to restore things if your disks are lost and replaced with blank disks. This may be more or less important to you depending on your business, but count on it taking at least as long for a full restore as for a full backup.
Good luck.