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Yes you can side dress your tomato's with compost .. Just make sure none of the compost is touching the leaves and the compost is well cooked .. If you have any low to the ground leaves snip them up a bit .. this will help prevent blight ..
It will actually promote better root growth for your tomato's .. I side step this by planting them deeper and filling in the holes with compost and manure
Other than a bout with blossom end rot that wiped out the first batch of tomatoes we have a winner. Turned out my blossom end rot issue was lack of water to the roots. Took care of that and we are seeing second round starting to be down now!