Is it possible to travel from the Dutch to the Polish Border on a "schönes Wochende Ticket"?

Note that the Schönes-Wochenende-Ticket is valid for up to 5 people, but on only one day (until 3 AM on the following day), not the entire weekend. For a single person it may not even be the cheapest option - even on the ICE there are "Sparpreis" offers, limited contingents of cheap tickets you can only get if you book early.

Whether it's a practical choice depends completely on your route - look it up on bahn.de, choosing the "Nur Nahverkehr" option. On some routes, it's not much slower than taking the ICE, on others the difference is larger, or you can't make it at all in one day.

maybe I'm just confused about the intercity naming. In The Netherlands intercities ride everywhere, whilst in Germany it may be a more "exclusive" way of traveling, like the ICE or Thalys...

Basically yes: the regional/local trains are inferior because they're slower. If tickets were priced purely by distance, people would use these trains only to get to the closest IC or ICE station - on many routes they would be underutilized and unprofitable while the ICs and ICEs would be overcrowded. The Schönes-Wochenende-Ticket allows Deutsche Bahn to improve utilization of the local trains.

Another interesting option not widely known (though probably not applicable to your situation) is purchasing a regular international ticket which is valid for up to one month including arbitrary stops. If you plan accordingly, you could visit multiple cities in Germany with a single ticket.

The complete information on this can be found here in German. The author also maintains this Facebook page in English.

Using a "Schönes Wochenende" or a "Quer-durchs-Land" ticket for such long trips is hardly practical. It makes sense if you are an adept of slow travel. It makes also sense if you are several persons and you want to make a real bargain. In the most extreme case, if you are 5 persons you could then travel all the way for 8.40 EUR per person!

The trip from Herzogenrath (next to Heerlen) to Franktfur/Oder on the Polish border takes 11h30 with 4 changes. Connections times are reasonable (between 20 and 38 minutes). I have chosen Herzogenrath just for illustrative purposes. What I say here is also valid for other border towns.

As a comparison, by allowing IC/ICE trains, the travel time goes down to 7h00, with 2 connections.

The Dutch IC trains are comparable to the German Regionalexpress (RE) trains. They have a similar frequency of stops and provide a similar level of comfort. The Regionalbahn (RB) trains stop more often than the RE trains. In some places, the same rolling stock is used. Hence they offer the same comfort.

There is a better option. It is possible to travel from Herzogenrath to Poznan (in Poland) for 39 Euros. You will travel using a mix of regional, ICE and EC trains. You pay less, you can travel further and have a superior level of comfort. There is also a nice feature with this ticket. You can insert intermediate stops which can last up to 48 hours each. Below you can see here the details of a trip with a 24 hours stop in Düsseldorf and a 48 hours stop in Berlin. If in addition you find a return ticket for the same price, you will be able to travel 3 cool cities for just 78 EUR.

The following discussion can also be relevant for your purpose:

How to travel (relatively) cheaply by ICE trains in Germany?