Òf course a simple blood test could let you know if the horse is doped up .
No, it can't. The rest of your post is accurate, but this isn't at all true. You would have to know what drug specifically you believe the animal had been given and then you would need to test specifically for that drug. Depending on the time and the chemical, blood may not at all be the right sample either. There are NO tox screens, it doesn't exist. You have to specifically test for chemicals and toxins and these tests are pricey and often inaccurate.
Save your time and money, listen to the rest of the advice given in Afterparty's post, and make sure you do a lengthy, contracted off site trial period following a complete vet check. Good luck!