Well, speaking as a West Virginian (not born, but certainly raised, rather like our titular Senator), I can field an opinion from a decidedly on-the-ground perspective as it were. I feel that the absense of Senator Byrd would most likely not significantly alter the political landscape of the state, as unions practically have, and have had for a long period of time, the state in a veritable strangle-hold. Similarly, the tradition of old-style Democrat party-machines is a strong one, something which goes a significant way towards dominating the political scene. Conversely, I feel that the absense of Senator Byrd would deal a fairly significant blow to the state's economic conditions over the past twenty-five years (not that they've been spectacular anyway). One of the few lifelines the state has had keeping it afloat after the worst of the mining bust has been Senator Byrd's status as "the King of Pork", something made possible largely due to his overwhelming congressional seniority. Without this pork, West Virginia's economy would likely be in even worse shape over the past two decades than it already has been, a rather frightening prospect.
Confessedly, much of the root of the problem lies in the state's longstanding economic policies. Policies which, to be perfectly honest, I have at times felt qualifies WV for an SSR on the end of its name

(and there are unfortunately a large number of towns in the state that would not look out of place in say, Albania

). However, these policy problems are things which can largely only be solved on the state government level, rather than on the congressional level at which Senator Byrd is a political actor, making his absense likely to be of minimal impact. It is, however, possible, that without the pork provided by Byrd the economic situation after the mining bust may have deteriorated to such an extent that either the Democratic administration would wake up to the need for economic reform earlier, or that it would open the window for a Republican coup.