If the TV has inputs for S-video or RCA (yellow) and audio (white and red) then this would be the preferred connection from the 625 to the TV, bypassing the TV's tuner completely.
If it's such an old TV that it doesn't have external inputs, the fact that stations stop broadcasting in analog will not affect the fact that your TV will still receive signal from the 625 on channel 3 or 4 (or the TV2 modulated channel for that matter). The TV's analog tuner will not magically stop working in Feb 2009, but local TV stations will stop broadcasting analog signals. Doesn't affect your reception from Dish Network in the slightest.