You are wise to look at how products interact as a system, but as long as you choose a good low-VOC adhesive you should be fine. VOCs, or volatile organic compounds, are chemicals that vaporize on contact with room-temperature air. VOCs are air-activated, not heat-activated, and they are mostly released when the glue is applied.
Many adhesives contain a solvent mixed with the glue. VOCs within the solvent cause it to evaporate as the product is applied, allowing the glue to spread before it "sticks." Since these compounds vaporize on contact with air, most will have evaporated by the time your radiant heating system is in operation.
Choose your adhesive by comparing the VOC information on product packaging or in Material Safety Data Sheets. Generally, you want to choose a product with VOCs of less than 250 grams per liter. A best-in-class construction adhesive would have a VOC content of less than 140 grams per liter.
For the subfloor assembly, I recommend using Bostik Home Heavy Duty Construction Adhesive, which is rated at 115 grams per liter. Another good product, OSI GreenSeries Subfloor & Deck High-Performance Adhesive, is less than 2 grams per liter.
Low-VOC adhesives created specifically for installing floor-surface materials include W.F. Taylor?s Envirotec Adhesive and CHAPCO?s Safe-Set Adhesives.
The type of radiant system you select should not affect the potential to release VOCs, but there are other environmental factors to consider. Some systems go above the subfloor and are embedded in lightweight filler; others are attached below the subfloor. I prefer the type installed above the subfloor, because the closer the piping is to the finished floor, the more energy efficient the system will be.