Hello Laurie,

Removing the young seed cones should not be a problem and as you mentioned,  it may just help the tree with growth. Some Christmas tree farms will use that method to decrease the energy from seed production and into branch and tree development. Caution when removing the cones as not to damage any branches. The main thing to remember is to keep your spruce adequately watered right up to the first freeze. The guideline of providing moisture is one inch of water per week when rains do not supply it and periods of drought.

I am including the following articles regarding pine cones that you may find interesting!

Fun facts about pine cones - MSU Extension

Spruce trees produce a bumper crop of cones - MSU Extension

If you have any further questions don't hesitate to contact Ask Extension!