There are two types of testing.... communicable diseases (usually only by big vet clinics, but all clinics should test for this because they are liable for it, as is anyone who sells it) and quality. If the colostrum is so poor it's milk, its really not worth giving. Would it HURT? No, but it wouldn't help at all. The most basic type of testing is a specific gravity test. Its basically a special float containing the milk suspended in a cylinder of distilled water. Depending on what level the float floats at is the milk's specific gravity. Scores of 1.08+ are good, and 1.03 are very poor (1.00 being distilled water). This operates on the concept of "the more dense the milk is, the more proteins (antibodies) it must have". Its a good system, but really not accurate. ARS sells a little handheld version (
http://arssales.com/equine/html/epfo-refractometer.html) that works on a similar premise.
Are you going to HARM the foal by giving whatever is in the freezer? 98% of the time, no. If you get it from someone else though, you should at least have it in the back of your mind "where did it come from, was it filtered at all, and is it worth keeping?" If you don't KNOW the quality of the colostrum, its a very good idea to give plasma. The trade-off is clean, tested, quality colostrum from a vet clinic is safe to give, and will satisfy the foal's needs. Plasma is artificial (to the foal), has SIGNIFICANT risk involved (plasma shock), is VERY VERY VERY expensive, and requires a vet to administer. Paying a little extra for quality tested colostrum can completely avoid (usually) the need for plasma and expensive vet bills. All I can suggest is get the best quality colostrum you can find at a local colostrum bank; test your foal's IgG as recommended by the vet (if you have a kit such as ARS's densimeter or the SNAP test, you can do it yourself on the farm at 12, 24, and 72 hours), and test your mare's colostrum as soon as she foals using ARS's refractometer or an "old fashioned" specific gravity test. Do all that, and you'll maximize your foal's immune system and hopefully minimize expensive, sometimes life altering (for the foal) issues.
PS: Some commercial colostrum banks also hyper immunize the mares prior to foaling, in order to "load" the colostrum with all kinds of goodies. Last I heard this was debatable whether or not it actually improved the quality, but it could possibly be a big plus to "groomed" colostrum banks!