I take it you're doing a short hop into the city? The short answer is no. MAD doesn't do clean non-Schengen arrivals (one of my biggest gripes of the airport as it could easily be set up to do so with a bit of signage and get more people walking past the shops). You can try to get through security at T4S before passport control but I believe they should deny you with a Schengen boarding pass (really very easy security process). I outlined earlier in this thread how it's technically possible to do it with an EU passport, but if you're not a European Citizen then no dice.

As far as the differences in the lounges, Velázquez (T4S) is notably larger and has some areas that are generally always quiet (particularly the restaurant area all the way to the left during the day when it's not in service) and a lot more lounger chairs. It also has much better views of the apron and get to see a lot of interesting planes taxi by in front of you if you're into that. Also, it's much quieter during the afternoon hours after the 1030-1300 rush to the US and early Latin American departures and before the late night bank when it starts to get crowded around 21h again. Dalí (T4 main) feels a lot airer as it is a terrace above the main terminal floor and doesn't have it's own ceiling. The food and drink between the two are the exact same so that's not a big deal. As I mentioned, there's a big bank of European flights in the afternoon so it can be quite crowded, especially between 16h and 18h. If you have Priority Pass, the AENA lounges are also generally quite nice, though I still haven't made it to the Plaza Mayor lounge since the renovation. That space is enclosed so will definitely feel a bit more cramped (but that's comparing to a terrace lounge). The pictures look pretty nice so might be another option to consider if you have a credit card that gives you access.