That really depends on what the status of your backup is, whether you can agree with them not to erase and information, or to try to recover information first, whether or not you are concerned that a replacement computer may come out and only be able to load a newer operating system, and how much faith you have in their refurbished parts that may be put in its place. Usually it is pretty good either way. Don't forget many logicboard repairs are due to people not knowing how to handle the ports and cableson their computer*:
http://www.macmaps.com/frayguide.html
Not that you are one, but it is something to be aware of.
- * Links to my pages may give me compensation.