It depends a bit on how big the curtains are and how big a load your washer will take. I have dyed lots of things before using washing machine dye.
Dyes will only work on the cotton (and possibly viscose) threads in the curtains so the overall effect will be a paler blue that the dye would normally give, with an even paler (possibly still cream) trim ( this should be fine if by "trim" they mean the curtain header tape). The lining may dye a bit darker than the actual curtain as it has a higher % of cotton in it. The thread used for sewing the curtains is most likely to be polyester and won't dye so any visible stitching will still be cream.
If this sounds fine to you, then you need to check the weight of each curtain and how much your washer can take. If your washer will take a curtain OK, then you should be able to dye it fine. Look at how much weight the packet says the dye can be used for. If your curtain is heavier, then the dye will again be somewhat paler than you think unless you use more than one packet of dye. If your curtain is a bit big for the washer it may work out fine but there is more risk of the dye being streaky.
Other things to think about.
If you are dying each curtain separately, then use exactly the same amount of dye and the same washer setting for each one as any variations will result in them dying to slightly different shades.
Pre-wash each curtain to get rid of any dirt/grease that may affect the absorbtion of the dye.
Check how sun-faded the curtains are. If patches are noticeably paler through fading, then the patches are likely to still be paper on the dyed curtains. If they are a very pale cream though and the fading does not result in much colour difference, then you may be fine.
Always follow the dying instructions exactly to avoid streaky or patchy dying. Some dyes need salt. Sometimes you can buy a packet of this when you buy the dye but if not, dishwasher salt is cheaper ( and works just as well) as table salt.
Dye instructions usually ask you to wash on the highest temp wash possible. Your fabric will prob be OK on 60 degrees but do think about the possibility of shrinkage, particularly if the linings are sewn in as they may shrink a different amount to the main curtain fabric!
Dying stuff always involves some degree of risk, but IMO half the fun is not knowing exactly how things will turn out!
If you would otherwise be chucking the curtains and you don't mind spending £15ish (maybe more - haven't bought dye for a while) on an experiment, then go for it!