It may depend on the type of sales.  For someone selling in a retail store, maybe not.  

For someone who sells a higher-end product that is one-on-one selling, social media can help build the relationship between the salesperson and the client.

Sure, but indirectely. Except if the "personnel's" is oriented to "sales".

It is complimentary relation, most of the time is may or may nor increase sales but it do gives advertisement that is promotion to the products among consumers so complimentary it may help which most of the times is does, however for all type of products it may be the effective for e.g. for a consumer with pathological condition he will consume/buy which has been prescribed product.

On the other under normal life cycle it do broaden marketing scope and to reach for more consumers. we met 10 people 2 choose to buy and one who contacted 1000 definitely chances are better for him to increase sales.

Working/busy professionals compare on social sites for selection which is becoming now days a big factor among other factors in their purchase, so for this niche segment the sales personnel's use of social media and sales performance can benefit to the maximum.

Thirdly Social media can be used in many ways , to elaborate

1. one can use it on social sited just for connecting with people where he is sharing social cause which can help him in building his brand image/trustworthiness

2. one can use it solely as advertising media for the product in question and reaching more customer base, he may be able to enhance sales.

3. Else he can use a combination of both

Giving a certainity on statistical measures like correlation coefficent is difficult as the behavior for purchasing will be depending upen "N" number of factors but surely it is one of the factor and important factor in today's scenario which is evident that every company whether it FMCG sector, electronics (mobile/laptop Televisions) sector, or manufacturing sector all are coming with twitter, facebook pages etc.

So definitely there exists a direct relationship between sales personnel's use of social media and sales performance for many commodities not for all

Definitely...there exists a non-formal network where every individual in the society is connected or gets influenced with those who may be near connected ones.There may  exist a social bonding of connectivity where opinions on brands,products and services spreads and influences the ultimate point of sales, where both customer and salesperson are involved.

Yes, however it depends on how the sale person use social media creatively and how to interact with the clients/consumers. Usually, sales performance will be upgraded by a good social bonding and marketing in social media.