Can Airport Extreme interfere with modem internet connectioin?

Is it possible in any way that the Airport Extreme device I am using can interfere with the internet connection on the modem?

It is very unlikely, but possible, that wireless interference might affect both the AirPort Extreme and Actiontec modem/router if both of them are providing a wireless network signal, the devices are located in close proximity to each other and they are not separated by at least 3-4 wireless channel settings.

But, even if this were the case, both products would be affected by interference. It would not be a case of the AirPort Extreme interfering with the Actiontec modem/router, or vice versa. Both products would be having problems if wireless interference were the issue.

An easy way to find out if the culprit is wireless interference would be to simply turn off the wireless radio on the AirPort Extreme as a test, and see how things perform that way for a day or two.

Or, if you don't want to turn off the wireless on the AirPort Extreme, simply power off the AirPort Extreme so that only your Actiontec device is providing an Internet and wireless signal.

If the problem continues, then you know that the problem is definitely not wireless interference......the problem is either in your Internet wiring connections or the Actiontec modem/router itself.

Moreover with a recent service interruption there was severe crackling interference on the voice line that stopped when the power to the modem was disconnected.

Wireless interference would not cause "crackling". Wireless interference would tend to slow down the wireless connections and in severe cases, it could result in a loss of the wireless signal.

If you do not plan to use the CenturyLink wireless, it might be a good idea to turn off the wireless function of the modem/router. Your call on that.