No-this does not necessarily lead to that. There are QUOTA for passholders on some trains-notably all FRench TGV and its lookalike same ones over the border, thus this €*. It may mean there are still very expensive normal seats and no cheap REServ only seats for passes.

You can check for this train via b-rail.

IF you plan to only do this trip-or maybe return, then a pass is not the best buy-only if at least 4 days of train travel on fairly long trips are planned.

In fact well over 90% of all trains here in EUR are without any need or even canNOT be REServed-but tipically passholders all want the very same others that do.

I’m planning to do more travel but the most expensive single way ticket is from Brussels to London and it’s the same price as the pass. It’s just that I don’t want to buy the pass if there is no seats. 
do you know if the Eurostar only allocates certain seats for eurail ? 
or is there availability as long as there is regular seats?

There is a limited number of pass holder seats on the Eurostar and on popular departures and during high season those sell out weeks, and sometimes months in advance.

The best place to see the availability of passholder seats on the Eurostar is 

https://www.b-europe.com/EN/Booking/Pass#TravelWish

Press "later trains" and eventually you will find the next available connection. 

If you have a mobile pass you need to generate a Pass Cover Number in order to make the reservation at b-europe. You do that here in the PCN generator:

https://community.eurail.com/news-and-announcements-39/pass-cover-number-generator-is-live-5653