No.
1) Need pump/ extra line for chiller.
2) Need something under your tote that's going to collect the large amount of condensation the chiller is going to create.(I'm assuming your indoors)
3) Your current feeding/watering line is too low, the base (especially if you're using clay) of your plant is going to dry out.
4) you're return line is too high, sediment, salts, etc.. are going to collect on the bottom of your bucket, also the condensation issue again is going to occur with your bucket due to cold water.
solution:
1) Ditch the chiller unless you really need it, look towards ventilation or hood cooling if possible.
2) Ditch tote for a 5 gallon bucket, and keep this feeding bucket Aerated. Switch to top feed/ watering with drip stakes or equal.
3) Position your return line where your air stones are located in your plant bucket drawing or on the side of the buckets as low as possible and ditch the air stones in the plant buckets. Raising your plant buckets will returns most water back to your feeding bucket. The higher the plant buckets, the less to almost no water on the bottom. This will give your roots Aeroponic suspension as long as you use clay pellets for the base, keep the plant bucket sealed from light, and water 2-3 times for 10-15 min during lights on. You can also install a line shut off valve on each return line to assure the plant buckets fill up and your roots become saturated before draining and beginning the next suspension period.