Unfortunately, it's probably not a Powershell issue. It lacks the redirect-in-from operator, but it provides a very big and fairly obvious error if you try.
```
PS> sqlite3 < this_doesnt_matter.txt
At line:1 char:9
+ sqlite3 < this_doesnt_matter.txt
+ ~
The '<' operator is reserved for future use.
+ CategoryInfo : ParserError: (:) [], ParentContainsErrorRecordException
+ FullyQualifiedErrorId : RedirectionNotSupported
```