You can expect a scaler to add at least 1 frame of lag, but that doesn’t matter if you’re only adding it to make it compatible with your capture device.
If you’re worried about lag using your capture device’s loop-out, add a video splitter earlier in the chain. If you have display that can take the analogue RGBS/RGsB from the PS2, toss in a SCART splitter (or something like the current gscartsw, which will rewrite RGsB to RGBS and make those format switches easier to manage); or, if you’re using a display with HDMI input, get an HDMI splitter (this thing, per this recommendation).