I was thinking about using back-alley brawl and the transporter ability. Would that be alright?

Here is the text of back-alley brawl:
Characters who make close combat attacks using no powers, feats, or team abilities and who are not affected by the powers, feats, or team abilities of any friendly character get +2 to their attack values.

You can get the bonus from Back Alley Brawl when using transporter move and attack as it's not a power, feat or Team Ability.