Upvote:5
Your itinerary is certainly doable in logistical terms, if rather tiring. So, if the altitude doesn't get you, you might still need some time to recover.
Aguas Calientes is an uninteresting little tourist town, so if you were thinking of staying a few nights, there, you would be much better off staying in Cusco instead, to adapt to your surroundings. If you go to Aguas Calientes straight and plan to go and see Machu Picchu the next day, and you do get hit by altitude sickness, or general travel malaise because of the long journey, you'll end up only blaming yourself.
My advice; stay in Cusco first.
Upvote:6
My brother flew from Lima to Cusco. It was brutal.
I took time in Bolivia, Lake Titicaca and then in Cusco before heading to Machu Picchu. It was still brutal.
Others have it worse, others have it less, but generally you'll be out of breath at the very least, and likely with headaches.
There's basically nothing to do in Aguas Calientes - some springs and food (which got us sick), while Cusco has a lot to look at, see, eat and do, including day trips to other ruins / old places.
The majority of tourists spend time in Cusco first, and there's a good reason for this.