The documents, which are compulsorily registerable, though not registered, are admitted as evidence to establish any collateral issues.  Please advice, whether documents which are not adequately stamped are admitted in the Court to prove any collateral facts?

There is vital difference between unregistered document and under-stamped document.  The unregistered document will be admitted as evidence to establish collateral issues.
But under-stamped document will not be admitted as evidence to establish the main issue or any collateral issue.  Section 34 of the Karnataka Stamp Act is very clear in this regard.  Such documents will be admitted as evidence on payment of shortfall and penalty of ten times that of the stamp duty.

For example an agreement to sell without possession clause attracts a stamp duty of Rs.200/- but was paid only Rs.20/-. The short fall is Rs.180/- and penalty is 10 times the proper stamp duty i.e., 200 X 10 = Rs.2,000/-. In all Rs.2,180/- to be paid, so that it can be used as a source of evidence.