Can I use a cyclocross jersey for gravel riding or road training?

Yes, with caveats. A CX jersey works well for gravel riding, especially in cool conditions, though you'll miss the extra pocket storage of a dedicated gravel jersey. For road training, a CX jersey is fine for winter base miles but may be too warm for summer rides and lacks the aerodynamic fit of a road race jersey. The minimal pockets are the biggest limitation for training rides where you carry more gear.