I don't see how they could be associated
Your tire is mounted to your rim. The rim is mounted to the wheel hub. Your break disc would be, in many cases, mounted by tightening the lug bolts to your rim. The rim would press against the disc to tighten it your hub.
The clicking sound you are hearing could be related to the work you had done but would not be related to the slow deflation of your tire. The brakes do not interact directly with the tire in any way.
The deflation of your tire could be discovered through visual inspection. Check all the tread and sidewall area for screws, nails, etc that may have penetrated the tire. Additionally, you could use a bucket of soapy water and a rag after inflating and apply the soapy water everywhere to check for air bubbles from a leak. Check the following.
Tire bead - along the edge of the tire where it meets the rim.
Valve stem - You may have a faulty valve stem where it meets the rim OR the schraeder valve inside the valve stem. Take the cap off the stem and see if it's leaking there with your soapy water.
All over the tire - Slop the soapy water all over the tread and sidewalls to see if you can find he bubbles
There could be numerous reasons for the clicking sound. If you have a speedometer cable (unlikely), all the way to some brush caught up in your wheel. You may want to jack up that tire and spin it to see if you can discover the location.