of course, but it will depend on the enzyme. For instance, you could immobilize a lipase using an hydrophobic support. This process does not require a purified enzyme preparation.
On the other hand, independent on your enzyme, you could immobilize it by using aggregation and cross-linking (CLEAS). This, procedure does not need any purification- Even though, you could design the precipitation step to remove some impurities.
Yes, you can utilize a crude enzyme extract for immobilization. I complete agree with Carlos Vera, you can go ahead and prepare CLEAs for the enzyme of your interest.
Please find the recent paper from my research group.
Article Extraction and crosslinking of bromelain aggregates for impr...