The two words can be strung together just fine in English. Think of the word "rub", then "rubs", then "rubs search", then "rubsearch". The final 'b' in "web" is indeed pronounced differently when linked to the word "search".

For more discussion see:

https://en.wikipedia.org/wiki/Sound_change

https://en.wikipedia.org/wiki/Assimilation_(phonology)

Page 10 of http://www.ling.hawaii.edu/faculty/donegan/Papers/201Xhistph...

They can but it's more difficult on a muscle level. You have to change the position of your tongue quite a bit to alter the airflow transitioning from the bilabial plosive to the sibilant, versus "Google" where you can almost say the G-L transition without moving your mouth; just a very slight adjustment of your uvula and tongue can produce an understandable sound.

Try saying "web search" without moving your mouth. Now try saying "google" without moving your mouth.

It is not normal English for a "b" at the end of a word to get assimilated into the "s" at the start of the word.

(Note also that when you say "rubs", the "b" is not getting assimilated - it's the "s" that is getting assimilated into a voiced "z")