In general, I do not expect several to start with two, just as the dictionaries state:
- several adjective
being more than two but fewer than many in number or kind:
several ways of doing it.
- Several is used to refer to a number of people or things that is not large but is greater than two.
I had lived two doors away from this family for several years.
Several blue plastic boxes under the window were filled with CDs.
What specific number you expect or imagine depends on the context. But generally speaking, it will not be two.
For context, here is a little diagram for comparison:
Couple < few < some < several < many
That's how I see it. With couple, I expect two, or about two. In other words, it can be two. But not with several.
Note that the diagram is not meant to be a strict rule. Because these terms are not defined concretely (e.g. 5, 10, 21, etc.), their usages are flexible and there is occasionally some overlap. For example, one could say a "couple" when there are actually 3 or 4 of something. That could also be a "few".