Can I drive from Belgium to Sweden without a valid Schengen visa?

I know this isn't exactly what you're asking, but the optimal solution is to receive a temporary Schengen visa from the Belgian authorities that would allow her to travel within the Schengen area without worrying about spot checks. AFAIK all Schengen countries can issue one for the duration of the residency permit processing period, as they don't want people stuck in the country for an indefinite amount of time. For example, Czech authorities call this visa sticker a "Bridging label".

I have asked a separate question here on how to obtain such a visa sticker from the Belgian authorities.

Sweden suspended Schengen automatic freedom of movement between Denmark and Sweden in January 2016, and then partially lifted that suspension in May 2017.

However, they still require ID and proof of eligibility to enter Sweden, which is established on arrival at the Swedish side of the border (previous restrictions required checks before travellers left Denmark).

These checks were prolonged in November 2017.

I wouldn't risk it.

Denmark has spot checks at its land border and ports, but these are quite rare (although as mentioned in a comment, they are reportedly becoming more frequent).

As for Sweden, they stop almost all buses at the Öresund bridge, and perform checks on selected cars (though most are waved through).

The best bet would be to either:

1. take the Helsingör-Helsingborg ferry or a ferry from Travemünde or Sassnitz to Trelleborg. At the ports of Helsingborg and Trelleborg, few cars are stopped.

2. (safest) Fly on a non-low-cost airline to Sweden (such as Brussels airlines to Bromma), and with only hand luggage. There won't be any border checks, and at the gate the boarding pass is normally enough, or sometimes they may look at the passport ID page to identify you as the ticket holder

When I crossed the bridge from Copenhagen (Denmark) to Malmo (Sweden) on my car with Russian number plates in 2015, I was stopped at the Swedish side and we had to show our passports, tell the officer our purpose of the visit, plans for the trip, etc.

So the border checks are definitely real. Probably if your number plates are from one of neighboring countries, you have much less chance to be stopped, but I wouldn’t bet on it.