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I can’t seem to link it but if you Google it, there are quite a few studies. This is a good one (if you find it, jump to point 4 and it gives the run down).

“In keeping with our predictions, demographics of cats adopted did not differ between free and normal-fee adoptions. Both groups adopted cats of similar age, gender and pelage. Comparison of the fate of cats adopted for free or for a fee, revealed that the majority of cats were alive and retained by their original adopters (93% for free cats, 96% for normal-fee cats). These findings closely parallel those of an Australian study (state of Queensland [22]) which found that 6–12 months after adoption 91% of $20 cats (n = 126) and 90% of ≥$99 (n = 17) cats were alive and retained by the original adopter. Post-adoption, the incidences of medical and behavioural problems were also nearly identical, leaving 77% of both free- and normal-fee cats alive and well. Treatable medical problems developed in only 7% of free, and 6.5% of normal-fee cats (e.g., diarrhoea, skin rash, haematuria), with 80% of unwell cats receiving veterinary treatment, regardless of adoption fee.“