Here's my opinion on the first part of your question, does eagle's vote have any effect on other regionals, specifically Skywest? If so, why?

Short answer: Yes
As to the why: American Airlines (AA) stated that it would award contracts to regionals other than American Eagle if the TA was voted down. If American follows through with the threat then other regionals like Skywest, Mesa, Republic, etc. will get the contracts that Eagle was supposed to receive if they took it up the rear end with a concessionary contract.

Here's what I think, not that you asked. The Eagle pilot group did an awesome thing today by voting no. They have made a statement with which the majority of regional pilots will agree. In essence, the statement being we are tired of getting the skin worked off our backs for minimum wage while profits abound. We are worth more than that and are in a position to leverage our profession.

Republic has a similar vote pending. I think the vote closes on April 4th. If the Republic pilot group follows suit, there will be a definitive message (ripple) sent across the industry.

That's my 2 cents worth.