No. Most likely they won't. Here's what we do to address the issue:
LinkedIn invites are always custom. So instead of the default message ("I'd like to add you to my professional network on LinkedIn”), you’ll be sending out invites with your customized message.
This message will also be personalized. Meaning it will include the person’s information such as first name (as well as location, title, and company name in the future)
We have the experience of growing a product from 0 to 150M users. We’ve used such techniques (similar to those being used today on LinkedIn) to drive the growth of that product. So we’ve gained a lot of experience in user psychology and user behavior, and we bring that to the table when it comes to helping our clients creating and optimizing their campaigns, the messages copy, and the search queries.
Bottom line? People receiving your messages will believe that it was sent by a real person.