Honestly mate, the answer is no.
Was the squad last season better than his first, yup, is the squad this season better than last - again it is. Is that being reflected with the teams 'improvement' - nope, the team if anything is regressing in terms of results.
You for example could put Moyes in charge of Barcelona and eventually they would play dour and defensive minded football and they would start to regress, you could put Martinez in charge of Barca and they would attack without a thought to pressing the opponent or defence and they would start to regress.
Right at this minute Martinez has a defence comprised of 3 England Internationals - Stones, Jagielka and Baines, and Argentinian international - Mori, A Republic of Ireland international - Coleman, all of whom are highly rated, he has a young highly touted player in Galloway in addition. and collectively they can't defend to save their lives, they are protected by two holding midfielders in Barry and McCarthy who are both highly rated and praised as quality players, and still we can't defend to save our lives.
You could put Martinez in charge of any team in this league and within 2-3 seasons they would start to ship 50-60+ goals a season. We need to stop trying to kid ourselves that this is some form of long term project and when it clicks we will be winning every game 5-0 with 100% possession, we can't defend under Martinez, arguably he has never had a team able to defend - was gifted his one defensively good season by the fortune of following Moyes regime, people have quoted the job he did managing to keep Wigan up for a few years, ultimately the way he did that by playing attacking footy isn't sustainable for any degree of success without a strong defensive foundation and long and the short of it we hired a manager who FAILED at Wigan.
Their are many managers out their that could do a better job than he can do from this point onward