Yes to plot your customers on a map in Qlik Sense you need to convert their address into geographic coordinates such as latitude and longitude. There are several paid services which can provide coordinates and even area polygons for zip codes. I think Qlik Data Market can have coordinates for several countries so that may be worth checking out.
If you have a tight budget or just want to try mapping in Qlik Sense I recommend using Google Maps API for converting your adresses to coordinates:
You need to login with a Google account and get an API Key that will be used in your API request. The Google Maps API supports http(s) request which can be handled by Qlik Sense (as a web file data source) and the request will return a XML file where you can filter out the latitude and longitude for the adress (or search term) you have requested.
For example to get the coordinates for the city Malmö in Sweden I can use this https request:
Since it's not practical to set up a data connection in sense for every customer you need to disable Standard Mode in Qlik Sense (See 'Disabling standard mode' chapter in Qlik Sense help) so that you may use a variable and $-sign expansion for your address part of the request:
Finally you put the request string in a loop where you run through your customer's adresses and save the latitude and longitude to a table that you can use in your Qlik Sense Maps!
Note: The Google Maps API have a limit of 2500 requests per day (as of August 2016) with options to buy more. But that would be enough for most applications I guess..