That would be interesting depending on what LDs your child has. Those would be brain scans i would truly love to see. As an archaeologist i love looking at various scans both of modern people and people who croaked several million years ago.
But brain scanning for LDs, is interesting not all LDs show up in scans. For some, there is absolutely no legitimate evidence of anything concrete and organic that has yet been presented. Therefore, in such a case, no one will be able to see anything in such a brain scan. Still it might be worth while to do even then as the repetoire of brain scans and other evidence that is collected for use in finding whatever it is (unless ofcourse it really is nothing but a reflection of a poor home life or something which in some cases is really the ld rather than any legitimate ld.) So the more information that can be gathered, the more will be learned and the more there is to analyze in a search to find these things or to disprove them.
But, times are also very hard. If i were you, what i would do is i would first look into the varieties of LDs your child has. Ask the experts what they should see in the scan *exactly*. And if they say "well we don't know that it can be seen in a brain scan for certain....." Say to them you will get back to them and do your own research on the matter of weather or not it can be viewed in a scan. If not, in tough times paying for something like this when nothing can even be seen that is known to for a fact legitimize an LD.... Maybe then now isn't the time? it depends i suppose on what you think is the best course of action. But have the doctors show you on a picture of a brain, (maybe one in a medical text book or something) where and what they expect to see in relation to your child's LD diagnosies is the only advice i have.
I hope you do it though, because all the information that can be gathered that speaks to the legitimacy of various lds is really interesting... Torturing childrne making them stare at ink blots in some clinical environment that makes them nervois, seems a bit less relevant on a scientific level.
Best of luck making your decision!