I don’t believe so. I can’t find anyone offering ATE Insurance in Spain (unlike in England for sure) but Spanish isn’t one of my best languages. I believe ATE is not relevant in Spain because, according to Article 76 of the 1980 Spanish Insurance Act, a third party who has sustained a loss covered by an insurance policy may bring a direct action against the insurer. This use of Article 76 to support direct civil liability is made under the assumption that Spanish substantive law is applicable.
In the UK, the ATE insurance business was created to cover the needs of “no win – no fee” legal firms who wanted to mitigate their potential loses if the judgement is against them.
If you have good Spanish, I suggest you trawl some Spanish Website to make sure.