Of course HR would increase with work!!!
The only advantage of having a low basal HR in trained athletes is to have a higher reserve ( if your basal is 55 b/m then you can increase your HR 4X when you reach 220 while having a basal HR of 100 b/m would give you only another 100 (just 2X) with effort.
And if you mean by uptake oxygen extraction, then yes it will increase as the pressure gradient will increase with relative hypoxia of the tissues and the right shift of Hb oxygen dissociation curve ( lactic acid lowers the PH, high PCo2).