Yes. Each puzzle is built from its own numbers, so the target can always be reached exactly. After you submit, the page shows a shortest solution.
Yes. Every Daily Target can be hit exactly.
Why it is guaranteed
The puzzle is made backwards. The generator deals six numbers, then makes three or four legal moves with them at random, using +, −, × and ÷. The result of the last move becomes the target. Because the target came from the numbers, at least one route to it always exists.
Targets that could be reached in two steps or fewer are rejected, so you will not get one that is an obvious sum or product.
Your route does not have to match
There are usually several ways to reach the target, and only one is the one the generator used. Any legal route counts. Fewer steps rank higher, as explained in how Daily Target is scored.
After you submit, the page shows a shortest solution so you can compare. If you finish short of the target, you are not missing a trick that never existed. See the strategy guide for ways to find it.