Answer no. They could be healthy but so could a pedigree.
I've only had one cross breed a lucher & he died at 15 months. Of my pedigrees One has died at 4 of cancer but the vet thinks this was related to her being poisoned, 2 died of bloat,one at 4 & one at ten.three have died of cancer at 10,& one at 13. One died of a stroke at 14 one of torsion without a bloat at nearly 16 & one died at 16 of what the vet called old age. Untill their fatal illness only the bitch who was poisoned & the dog who died of a stroke were ill with anything major. He had CDRM & an eye problem but as he was a rescue at ten I don't know his previous history. Note these were GSDs none has hip problems in their lives though two had high scores that I know of & there was no such scheme when my first three shepherds were around.
My niece who has a comple heinz has many problems with it, the worst being a heart condition.
If I were going on personal experience I'd say that pedigrees are healthier but I know its really pot luck though picking wisely does lengthen the odds.

I agree with most of the previous posts. Not necessarily.
It is a lottery I think with most dogs and you can never guarantee that they will be illness free throughout their lives.

I have been exceptionally lucky in that in the last 20 years all my dogs have lived beyond 14 with no serious illnesses, including a pedigree irish setter, with only my Border Collie suffering from arthritis in his later years. Meggie, my staffie x who is 12 this year was put on antibiotics last month after having fatty lumps removed and that is the first time she had been on them. I'm banking on her living at least another 5 years.

Eye problems - I am not well up on these but it would be wise to check if any are common to both breeds and if both parents have clear tests.

Both the BSD and the GSD are on Schedule A for HC and thus all breeding stock should be eye tested annually, something that VERY few breeders of either breed actually do!

Hmmm..... all the BSD breeders I know check their breeding dogs annually.

I'd say the order goes like this, from healthiest to least (on average).

1) A fully health tested pure bred OR first cross dog (as in, both parents were different pure breeds, and all health tests for both breeds were tested for)
2) A non-health tested cross-breed
3) A non-healh tested pure breed.

The reason I would argued that a non-health tested cross-breed on average will be healthier than a non-health tested pure breed is due to genetics. Many (not all) of the genetic disorders found in pedigree dogs are recessive, meaning that both parents must carriers, or affected, in order for the puppy to inherit the disorder.

Therefore, recessive genetic disorders WILL NOT be passed down to a crossbreed unless both breeds have that genetic problem. If one breed does not suffer from that problem, it cannot be a carrier, and it is impossible for the puppies to have the disorder.

I don't know much about specific disorders, so I will make up an example. Imagine there is a genetic eye disorder that only poodles have. If you cross this poodle with a labrador, and do no health tests, you can still be sure the puppy will not get the eye disease, as both parents would need to carry the disorder in order for it to be passed down. If you crossed two poodles without testing for the eye disorder, the puppy may have the disorder as both parents may carry it. So crossbreed dogs are at risk from fewer diseases than non-health tested purebred dogs. For example:

1) Fully health tested dogs are at risk from disorders that cannot be tested for only ONLY.

2) Non-health tested crossbreeds are at risk from disorders that cannot be tested for AND SOME genetic disorders related to the breeds - it is impossible for them to get certain genetic disorders as both parents will not carry it.

3) Non-health tested pedigrees are at risk from disorders that cannot be tested for AND ALL genetic disorders related to the breed - both parents are from the same gene pool so may carry the gene.

The number of diseases that a non-healthtested pedigree is at risk from is greater than a non-health tested crossbreed. The risk of inheriting a genetic problem is greatest in non-health tested pedigree dogs. Rather than 'healthier', I'd say crossbreeds have 'less risk' when breeding without health tests.

Sometimes they breed dogs like pug with another breed to lengthen the nose so they don't have breathing issues (or as many/severe) which to me would suggest a pug X would be healthier than a pedigree pug. This may not apply to all breeds though.