...in a variety of contexts, so it's a little difficult to draw any conclusion from these. Some relevant passages for this discussion include:

Mr. Darcy says he wanted 'preserve my friend from what I esteemed a most unhappy connection.' (re: Bingley & Jane)

'A most suitable connection everybody must consider it, but I think it might be a very happy one.' (Lady Russell re: Anne & Mr. Elliot)

Henry was convinced of his father's believing it to be an advantageous connection (re: Catherine Morland)

'A very desirable connection on both sides, and I have not a doubt of its taking place in time.' (John Dashwood on Edward & Miss Morton)

The word seems to be used in many cases to speak of worldly considerations, but also those of emotions/personalities.

I've linked the string search if you want to explore this further.