That will work, but I think the better way would be BTS Ari to BTS National Stadium, changing trains at BTS Siam.
At BTS National Stadium when you exit the train you can use the skywalk which is linked directly to the MBK Centre so you will not have to descend to street level. This would mean this whole section of the journey from BTS Ari onwards would be by Skytrain.
You would join the BTS at Ari station N5, and catch the train heading towards Kheha. Disembark at Siam station CEN. You will disembark on Floor 3, platform 1. You need to go up the escalator to Floor 4, platform 4 and catch the train heading towards National Stadium station W1. As I mentioned, when you exit BTS National Stadium just follow the skywalk signs to MBK. The skywalk joins MBK in two places. If you can't walk up the steps at the first entrance then keep on walking on the skywalk and use the second entrance.
On your return journey, exit MBK and join the BTS at National Stadium station W1, catch the train heading towards Bang Wa. Disembark at Siam station CEN. You will disembark on Floor 3, Platform 3. You need to go up the escalator to Floor 4, platform 2 and catch the train heading towards Ku Khot. Get off the train at Ari station N5.
You can buy 1 single ticket from Ari to National Stadium for 37 baht, and the same price for the return journey. Believe me, it's not worth walking from Siam to National Stadium to save literally 4 baht each way.
The change at BTS Siam sounds complicated, but it's not. Each floor only has 2 platforms, and the platforms are either side of the same island. The most important thing is to know what floor you need next and the direction your train will be heading in, as all the signs will say "towards Bang Wa" or "towards Ku Khot", etc.
I hope that helps.