Differentiating UX from marketing here is tricky. I'll assume that this is effective in driving sales or the marketing department wouldn't be sending out the emails.
These emails are an alternative to the promo-codes that many sites use, and can in effect be seen as automatically applied promo-codes. So it's probably worth looking at the experience of them in relation to promo-codes. What's the experience of promo-codes?
- If you have one you feel happy and get satisfaction when you reduce the price.
- If you don't have one you might search for one on or feel like you ought to have one. Customers can learn to look for them on sites like myvouchercodes.co.uk etc. and they can find out of date codes leading to frustration.
- The box to input them prompts customers without them to feel like they are missing out. This causes drop out.
Promo-codes can drive traffic but generally don't lead to a great experience on balance. Sending an email where customers follow a link and the promotion is automatically applied has a subtly different experience:
- The offer is more personalised - only the special people with the email can get the offer.
- Items 2 & 3 from the list above don't matter any more.
So generally automatically applied promotions offer roughly the same happy path but without many of the negative experiences that promo-codes produce.
It's worth mentioning that over-using these types of offers can lead to customers being trained that they should wait until they get the next offer before making a purchase. Balance the short term wins against this carefully.