It most likely can be used (there is no "fruit of the poisonous tree" doctrine). Drawing on this analysis (I can't locate Nytt juridiskt arkiv 1986 online).
(Rättegångsbalken, SFS 1942:740) Chapter 35 Section 1 (35 Kap.) allows free "sifting, submission, evaluation" of evidence. Evidence can be rejected as insignificant. Specifically (following the analysis paper),
The Swedish legal system does not prescribe that it is
forbidden to present an item of evidence which the party has
got hold of while breaking the law. Neither is the court prevented
from ascribing such a proof a great value.
In one instance, blood was illegally drawn (only a doctor or registered nurse may legally draw blood). The Supreme Court ruled that
The fact that the blood sample was drawn by a laboratory
assistant does not imply such a divergence from the Code of Judicial
Procedure that it can be seen as a violation of the Instrument of
Government Chapter 2 Section 6. Neither has any of the
Swedish fundamental principle of law been set aside in a
way that prevents the submission of the blood sample.
"Surplus information" obtained by coercive means can also be used as evidence (i.e. information obtained incidentally, not related to the crime in question). Some limitations seem to have been recently imposed, taking the form on tightening warrant requirements and data retention.