Yes, URLExecute does work for "POST" requests. As an example, try using it with a deployed FormFunction:

In[5]:= co = CloudDeploy[FormFunction["x" -> "Number", #x &]]

Out[5]= CloudObject["https://www.wolframcloud.com/objects/ee2e4ae6-\
8d6d-48a8-b720-150720c21de3"]

In[6]:= URLExecute[co, {"x" -> 4}, "Method" -> "POST"]

Out[6]= 4

Using the default method ("GET"), the form is returned instead of the result.

In[9]:= URLExecute[co, {"x" -> 4}]

Out[9]= "x

   Submit"

Unfortunately, the API "Test" for POST is broken (and has never worked correctly). The good news is that it's not hard to do with Wolfram Language.

The Content-Type can be text/plain, since I'm assuming that you want to add numbers. It can be set to anything that Interpeter can handle (e.g., for images, image/jpeg).

Using URLFetch, we can specify the method as POST. The full call looks like this:

URLFetch["https://www.wolframcloud.com/objects/53543d2e-ccac-4d6d-baab-36a32b95c40e/myFunc", "Method" -> "POST", 
 "MultipartElements" -> {{"n1", "text/plain", ToCharacterCode@"2"}, {"n2", "text/plain", ToCharacterCode@"3"}}, 
 "VerifyPeer" -> False]

Note that if you're using a version of Mathematica prior to 10.0.2, you need to change "MultipartElements" to "MultipartContent".