Not really. In that case, it's more like a preemptive "Your welcome" before you say "Thank you". Since it is more literally "If it pleases you", they use this in places where in English you would say "Please" and "Your Welcome". For example, it's common for waiters to say this when delivering something to you regardless of if you have said "Dank je wel" (or variant) already or not. So you do sometimes find yourself saying "thank you" after they've said "your welcome". :)
As an expat, it appears to me that alstublieft is most often used to mean:
here you are when offering something and
(if you) please when asking for something.
And, then, as noted below, there is graag that means:
please when being offered something, and
gladly when the subject enjoys doing (the action).
though there is broader usage. The Dutch use these words quite a lot.
does someone know how its pronounced the "U"? Im a spanish-speaker and i have been told that is like pronouncing a "I" (in spanish) but with the mouth to say a "U"(in spanish). But it sounds very weird to my spanish-ears jajajaja, can someone confirm me what i said about the pronunciation please? thanks!!! PD: or maybe a trick to pronounce it good to non dutch-speakers