actually, as said, it's pretty simple since all the stuff is already implemented for Rle:

## that's like the boxplot.stats function... just for Rle...
rleboxplot.stats <- function( x, coef=1.5, do.conf=TRUE, do.out=FALSE ){
    quants <- quantile( x, probs=c( 0.25, 0.5, 0.75 ) )
    iqr <- quants[ 3 ] - quants[ 1 ]
    if( coef > 0 ){
        Ranges <- range( x[ x <= ( quants[ 3 ] + coef * iqr ) & x >= ( quants[ 1 ] - coef * iqr ) ] )
    }else{
        Ranges <- range( x )
    }
    n <- length( x )
    conf <- if( do.conf )
                quants[ 2 ] + c( -1.58, 1.58 ) * iqr/sqrt( n )
    Vals <- list( stats=c( Ranges[ 1 ], quants, Ranges[ 2 ] ),
                 n=n, conf=conf, out=numeric() )
    return( Vals )
}

## primitive boxplot function; works with Rle's and also numeric vectors.
rleboxplot <- function( x, range=1.5, ... ){
    ## have to make a matrix of stats...
    Vals <- rleboxplot.stats( x, coef=range )
    stats <- matrix( 0, nrow=5L, ncol=1 )
    conf <- matrix( 0, nrow=2L, ncol=1 )
    stats[ , 1 ] <- Vals$stats
    conf[ , 1 ] <- Vals$conf
    z <- list( stats=stats,
              n=Vals$n,
              conf=conf,
              out=Vals$out,
              group=numeric(0L),
              names=NA )
    bxp( z=z, ... )
}

## define a method boxplot for the Rle
setMethod( "boxplot", "Rle", function( x, range=1.5, ... ){
    rleboxplot( x, range=range, ... )
} )