When I was shooting my kid playing LL baseball, most games were played during the days, because the smaller fields had no lights, so this was not problem. Until the reached 14 all games during the weekdays were nights and tournaments on weekends covered day and night. Plus the bigger field 200mm is too short. Having said that putting a 1.4x TC on a 2.8 lens gives you more reach but you lose a stop (f4) I think this is too slow for twilight and night games. and if your in my situation or close to it where night games are half the regular season f2.8 is the way too slow, unless you live with ISO 12,800 and that can still not be enough pending the lighting of each field.
Canon 7D / 50D (40D premature death. Long Live Canon)
70-200/2.8 - 135/2.0 - 100/2.0 - 85/1.8 - 35/2.0
EX 50-500 - EX 120-300/2.8 - 18-200OS - EX 18-50/2.8 II - EX 50/1.4
TOKINA 12-24/4 (for sale1) - TAMRON 28-75/2.8, 17-50/2.8 - Samyang 8/3.5
KENKO Pro300 2XTC - 1.4XTC