Amazon Echo Lands On Teardown Table, Opens Easy But Tough To Reassemble
In a word, yes. The nimble fingered folks at iFixIt said there's just a little bit of stickiness holding the bottom rubber lid in place, which is easy to peel away. Underneath are "four impressively long T10 screws" tasked with holding the bottom stage of the Echo rocket in place. So, if you can use a screwdriver without poking your eye out, you should be good to go.
In a rocket like fashion, there are several stages to the Echo, most of which are relatively easy to remove. It can be a little tricky disrobing a swath of fabric that encircles the innards, but with a little knife work and some careful peeling away of double-stick tape, you'll be in like nobody's business.
The part that's truly tricky is keeping track of all the modular parts and pieces you took apart. There's even a gearing system inside, plus a bunch of other big and small components.

In the end, iFixIt gave the Echo a 7 out of 10 Repairability score, noting that the speakers (which are most likely to fail of all the parts) are replaceable and that separating components across three circuit boards helps improve modularity. However, it's a "fairly complex device," and since there's no repair manual, putting it back together can be a difficult chore.