Yes, scarcity apps really do help with conversion, as long as they aren't too intrusive for the customer. I would pick a subtle option, like https://apps.shopify.com/smar7-scarcity-timer, as this doesn't interfere with the user experience, but will help tap into the psychology of scarcity. Typically, I've seen the best results when the countdown starts at "Only 10 left!", but you should also consider the total sales on each item per day when creating this number.
You can make use of scarcity in sale-off days. One app which can create scarcity is Discount Best app. You show a countdown clock or a stock countdown bar. Combining discount and scarcity is a good idea.
Scarcity can definitely work, but only I only suggest using an app if there is true scarcity. There are a lot of apps that create fake scarcity, with meaningless countdown timers, or fake quantity counts, but most customers can see past this. When they do see past it, it creates distrust with your brand.
Some ways to create real scarcity is offering a 'Flash Sale'. Maybe this a 24 hour or less sale. Then you can have a countdown timer on your website or product displaying how much time is left of the sale.
Another option is offering a 'timed sale' upsell or cross-sell after checkout. In this case, after the purchase of let's say a coffee maker, you can offer discounted coffee grinds that expires 2 minutes after the initial purchase of the coffee maker.
This is what a flash sale would look like with Bold Discounts.
You can grab a free trail of that app here.
This is what an upsell after checkout would look like with Bold Cashier.
This is a free app you can grab here.
I hope that helps! If you have any other questions just let me know.
The "scarity" will work when you provide the genuine deal and information. Let's say you sell the exclusive set of products and items are limited. So when you put the "countdown" under the pricing it gives the value to buyers. He would know that if he won't do anything he will miss the deal. It's more about FOMO effect. Fear Of Missing Out. When you provide such information, the buyer would see the transparency of your brand and increase "trust factor".
With "scarity" factor I love to put "how many people visited the product Today" or "How many visitors are online NOW". In that way, you provide genuine information for the buyer, so he would have to decide right away or miss the deal.
For any products the conversion rate is different, so you need to TEST the store. Btw, make sure that you installed Google Analytics, just to see the difference with Shopify Analytics and understand better about "Conversion Rate".