No, it would create even more partisan gerrymandering, and it would be a huge gain for Republicans. Why? Because they would still get all the votes in overly-represented small states like Idaho and Wyoming, while the Democrats would have to split the EVs in California, NY, Illinois, Pennsylvania, etc. Bush would have won by about an extra 20 EVs in 2000 if the votes were distributed this way.
IIRC, Bush would have won in 2000 if EVs were district-by-district with no "bonus" EVs for senators.
Even without the "overly-represented" factor (no EVs for senators), Republicans still have an edge.
Yes, gerrymandering favors the Republican party in the US, just like it favors the Labour party in the UK.