Yes, this does appear to be a spongy moth (formerly called gypsy moth). The link below will give you some valuable information on this pest, how to ID it, and ways to control it. Be sure to download the file near the bottom re. Btk. 

https://www.canr.msu.edu/ipm/Invasive_species/gypsy-moth/index

While spruce is not their favorite host, the link below explains that when populations are very high, or when oak and other preferred trees are limited, spongy moth will eat evergreen species including pine, spruce, and hemlock.

These caterpillars will be actively feeding for 6-8 weeks and then pupate. In July the moths will emerge from the ground, mate and lay eggs for next year's larvae.

https://www.canr.msu.edu/news/gypsy_moth_caterpillars_damaging_spruce_trees

The best spray control is Btk, which is generally sprayed aerially due to the height of oak and other affected trees. Your local county may have a spray program available. Contact your township or county office and inquire.

https://extension.entm.purdue.edu/publications/GM-4/GM-4.html

The use of sticky tape around the trunk of your tree may help reduce their numbers. This, of course, works better for hardwood trees than for conifers. But certainly worth a try if you have a large number feeding on your spruce tree.

The links above should give you all the information you need to control these critters and also tell you how to report large numbers of these pests to county or state pesticide applicators.

Good luck!