Please advise if this is doable:
1) Landing at Barcelona airport at 10:05 in the morning
2) Taking the train from the airport to Barcelona Sants train staion.
3) Taking the 12:10 train to Pamplona, arrivin at 16:06.
4) Taking the Alsa bus from Pamplona to SJPP, departing at 17:30.
If this will work out, I am planing to spend the night at SJPP and start the camino the next morning to Orisson.
The time appreciation looks okay (particularly the bit from Pamplona to SJPdP) but if your plane arrives even a few minutes late (a likely event) or there is an unusual line at border controls you won't make it.
I would allow a three hour window from time of arrival to time leaving the airport. You likely won't need that time but it does allow enough time for the usual travel delays associated with airplanes and airports to have confidence of making your train.
I have on more than one occasion been on flights that leave more than 3 hours late. I have been in customs lines that go for more than an hour.
That being said ... you might make it. Just be sure to have a plan 'B'
1210 train leaves Sants
You have 13 minutes to get from Rodalies train to Renfe train. There is likely a security screening ... so minimum 10 minutes is likely needed.
1157 Cercanias/Rodalies arrives Sants
1138 Cercanias leaves Airport Terminal 2
1133 Arrive T2 Cercanias/Rodalies station
1115 Arrive at T1 shuttle stop (*snap* it just left)
10 minutes every 4 minutes for shuttle from T1 to T2 (if you arrive at T2 you can remove this).
1035 You are off the plane and in line for customs. You have 40 minutes (including a bathroom break)
1005 Plane arrives (on time ... a miracle)