In short, no. Tortoises and hamsters have different needs for their habitats.
While some hamsters might live in the desert in the wild, any hamster you buy in the store will have been bred inside for so long that, among other things, they've evolved to live at a normal room temperature (60-75 °F / 16-24 °C).
Meanwhile tortoises simply haven't evolved. While they make perfectly good pets, and can enjoy human interaction, they still require the same habitat as they would live in the wild. This includes temperatures of 78-82 °F (26-28 °C) on the cool side, and about 90 °F (32 °C) in their basking area.
Most importantly, rodents chew on everything. They can't really be blamed for it, it's driven into their brains. But to a hamster, a tortoise's shell is just another thing to chew on. Plus the shells contain calcium, which no doubt will encourage the behaviour.
This thread was posted after someone's pet rat escaped from it's cage and found their tortoise, chewing it's legs to the bone. I'd like to say that's the first time I've heard of that happening, but unfortunately not. Rodents and reptiles are something that simply shouldn't be mixed.