Hi. Not sure if its a bug or intentional.

The pickup tower is 2x2 in size, but it only get power if the lower part is in the electricity grid.
Also when placing, it does not show the electricity grid, like other entities that require electricity to work.

Neither bug nor intentional, but game restriction.
An pickup tower (PT) is actually a "compound entity", making up by two entities.
One is the "chest entity" that provides the storage, and what player cursor can interact with.
Second one is the "radar entity" that provides the timer counting, animations (rotating part), and electricity consumption.
There can only be one interactable entity, so do you prefer to see the electric grid but not stored item contents?
(As an item collector entity, I believe item contents are the most useful / relevant data to show.)

There is no single entity type that can provide all the needed features.
These two entities are already the best combination I can find. (Unless the devs decide to release a new entity type that can do all the above.)

I see, thanks for the explanation!
I have no experience in modding, so it's nice to know the limitations.

I understand now why I can't see the electric grid when placing, but is it impossible to make the whole 2x2 grid accept power?

I have to investigate the power connection problem.
It is probably caused by the tiny off-grid placement, which is needed to prevent graphical glitches between the two entities.
It seems not having an easy solution for this, but I will try to look for a solution.

Just released 0.17.19 / 0.18.3 / 1.0.0.
All of them should allow you to connect power to any tile of the towers now.
I have also modified both parts of the compound entity. Highlighting the centre will show chest contents (as previous versions) and pickup range; while highlighting the rim part will target the "radar entity" showing the scanning progress.

As with the vanilla radar entity, highlighting it does NOT show the blue square power range visualization. But there is the cyan bracket around the tower indicating it is with pole connection.

PS: By investigating Factorio API this week, I have found out the selection priority properties. This allows me to set the chest entity having a higher priority, letting this update to become possible.