The earliness of cropping tomatoes from overwintered plants will be limited by how early the light levels necessary to initiate flowering are realised. Growing on a windowsill the light levels may not get to these levels until quite late in the spring. Worth doing, just don't expect any fruit for Valentines Day!
One problem you may encounter if you were to save tomato plant roots would be a lack of vigour, hence low yield, from second year plants. By creating new plants from cuttings you should be able to overcome this problem- even in our short season multi plantings of one variety, or one planting using different varieties with varying relative maturities, are employed to maintain volume production. I would suspect that anyone in California who keeps individual plants growing year round would also encounter this problem. Commercially, and among committed hobbyists, crops are grown year round but successional plantings are planted to maintain volume production. The genetic background of these outdoor varieties will not allow the constant extended production found among European greenhouse cutlivars (long season greenhouse production in Arizona, British Columbia and Ontario does utilise European greenhouse cultivars however).
