I asked about this a few years back when Fakku started selling figures. In short, no (at least for those illustrated postcards for Native figures).
"Unfortunately, the postcard bonus is not included in FAKKU store purchases of the figures, that is only a Native online store exclusive."
Aside from one figure that actually included a doujin as a bonus (Eri Otori which was never sold by Fakku I think), all of the Native Online Store figures only come with just an illustrated postcard as a pre-order bonus. If you subscribe to Fakku, you get get a 10% discount on figures (can easily cover the price of the subscription) which usually results in the total including shipping being cheaper even with the current exchange rates being 110+ JPY/1 USD (also assuming you use a credit card that does not charge a foreign transaction fee) as the Native Online Store's shipping fees are quite high and have steadily been creeping up. The Native Online Store also wants you to place separate orders for different figures ("If you wish to order other products,please make a separate order."), but you can combine multiple figures into a single order on Fakku to save on shipping. Do check to make sure what all of the pre-order bonuses are, but in the end, it's up to you if the bonus is worth it to you (like if the illustration is done by a favorite artist or it's of a favorite character or there are other bonuses in addition to the illustrated card that would make it worth it).
I have not seen if any other manufacturer (Skytube, Dragontoys, etc.) have pre-order bonuses, but so far I have not received anything extra included with figures from those manufacturers when ordered from Fakku.