Yes.
Otherwise it means effectively, that teams like Florida and Vegas without state tax have substantially more dollars to spend on FAs then teams like Toronto, Ottawa and Montreal. The salary cap system was meant to level the playing field; if you don't incorporate different tax rates then you are not doing this.
NHL needs to peg the base salary cap number (say $80million) to say just the US federal tax rate for the average player salary and then adjust the actual salary cap for each team based on the added state and provincial rates for teams because as it stands right now you have:
tax for players earning $3 million per season (rough NHL average salary): League high- 52.4% (Tor, OTT), Low- 38.14% (LV, FLA, TBL - there is no state income tax) That means the take home for a player with a cap hit of $3 million is really $1.42 million in Toronto or Ottawa vs $1.85 million in Vegas or Florida.
Tax for players with an $11 million per season cap hit (ie. Superstar caliber player range): League high- 53.22% (Tor, OTT), Low- 39.2% (LV, FLA, TBL)
That means the take home for a player with a cap hit of $3 million is really $5.14 million in Toronto or Ottawa vs $6.68 million in Vegas or Florida.
These are big differences in actual take homes. Across a roster it effectively means that teams in tax-free states effectively have around $10 million more in cap space to the teams in the most heavily taxed provinces or states. There is no way you can argue that this is not an enormous competitive advantage. A team in a state like Florida or Vegas (if the owner is willing to spend to the cap) can simply outspend everyone else... by a lot.
NOTE: grabbed these stats from The Hockey Guy who took the effort of doing this for all the teams by sorting though the Cap Friendly data.