Nice spot, and you'll be right next door to the albergue. In fact, this is the more "upscale"lodging offered by the Carbajalas.
Where are you arriving in Madrid? Airport, train station, etc. The trains leave from Chamartín station, which is easily accessible by both metro and the Cercanías trains (the commuter line). It's a very short ride (about 12 minutes I think) on Cercanías from the airport. But whether the Cercanías train stop is convenient to you if you're arriving at the airport depends on whether you are on Iberia or a partner (One World Alliance). Those planes all arrive in T4, which is where the Cercanías stop is. Other planes arrive at the older T1, 2, or 3, and then you'd have to take an intra-airport bus to get over to T4. In any case, it's not hard and there are lots of trains from Madrid to León every day.