I always do to the door price checking.
You'd be a fool not to.
I know there's generally a bit of a price hike, but how bad are the customs fees and so on when you purchase from the US?
It can be tricky but assuming it's a taxable item (new) then you are hit with taxes and the carrier will hit you with a handling fee. So that could add 20 dollars (us) to a hundred dollar item. When it comes to import fees it can vary wildly I have imported inclinometers and been hit with 35%. Most test related equipment is duty free but typically it will be cheaper to buy in country if under 250.00.
Korea, Japan run about the same, China is good for sub 50 dollar items but the same otherwise.
Digikey is very good, shipping is inexpensive and they have a system in place to pay all extras at the point of order. I can order on the west coast at 6pm and have it at my door at 9:30am next day (for the regular delivery).
Of course some items can be held because they fall under the category of restricted use. That can be a real problem but that is part of the game as well.