Is it possible to perform request to https using http-request phing task?
If no - what workaround could you propose? wget?
Yes, you are not limited to HTTP only - HTTPS works fine.
Examples are shown in the phing documentation:
<http-request url="https://accounts.google.com/"/>
Alternatively, you can use the curl adapter:
<http-request url="https://accounts.google.com/" verbose="true">
<config name="adapter" value="HTTP_Request2_Adapter_Curl"/>
</http-request>