Here's how the TPS fits into the picture:
* The ECM uses the TPS to determine throttle position. When the engine is cold, the ECM might command a slightly higher idle speed. A faulty TPS could send incorrect signals about throttle position. If the ECM thinks the throttle is open more than it actually is, it might compensate by *reducing* idle speed. However, this is unlikely to result in a *high* idle.
* Incorrect TPS signal could affect other systems that indirectly influence idle. If the TPS is sending erroneous signals, it might cause problems with the air-fuel mixture, potentially leading to unstable idle behavior, including potentially a high idle in some edge cases, but this would likely be accompanied by other symptoms like rough running.
* High Idle is usually due to the CTS. A faulty coolant temperature sensor (CTS) is a much more common cause of a high cold idle. If the CTS reports a falsely low coolant temperature, the ECM will try to compensate by keeping the idle speed high to warm the engine faster.
In short: While a faulty TPS *could* contribute to unusual idle behavior, it's much less likely to be the direct cause of a consistently high cold idle. The CTS is the prime suspect. Other possibilities include vacuum leaks, a faulty idle air control valve (IACV), or problems within the ECM itself.