No. For starters there is a connection between the D's, however not a familial one, at least not in this current age. So that's not something worth mentioning to indicate they might have been brothers as there are even giants who have the D and Roger himself married a D, so they are not brothers by blood.
Secondly Roger himself pretty much discarded the possibility in him being a 'brother' of Garp when he asked him to look after Ace. If they truly had been brothers, he would have used that as an argument to convince Garp, but instead he said something along the lines that they had killed each other almost so many times that they're practically friends or at least that he knows Garp well enough by now to know he would not let an innocent child die. That's the complete opposite of what you are saying as if they were 'brothers' why would Roger then refer to how many times they killed each other and not that they were once 'brothers'?
Thirdly a lot of D's have the tendency to get along with their enemies depending on their motives and personality. I mean Roger has shown that serval times with for instance Garp and Whitebeard. BB also a bit and above all Luffy (their are countless of examples of this, not in the least how Robin became a Strawhat). The whole 'enemy' business is for most D's quite an unusual concept. Same goes with their go with the flow and do some crazy stuff attitude. It's a trait a lot of D's have, not only Roger or Garp. Idem for their smile (BB, Saul). We all know that there is a connection with all the D's, however some of them are oceans and races apart. There is nothing that indicates that they are brothers.
Fourthly Garp was one of the strongest marines, however you still had Sengoku and Kong too, so it's questionable if he was really the number 1 of the marines in strength.
Fifthly if that really would have been true, we should have known it by now as there is something seriously wrong with the idea that at the same time Roger makes his way up as a pirate his brother is doing the same in the marines and the marines themselves wouldn't know that or care? Doesn't make much sense considering they had no quarrel throwing out Garp's son, grandson and Ace's history, but not that Garp and Roger were brothers? And them not knowing that would be weird too.
Personally I don't like the idea of them being brothers, whether in blood or in bond. That makes it repetitive as Ace and Luffy already had such a bond and it gives the impression all of them are in the same little group, while currently they are all separate and were Ace and Luffy the unique ones. There's also no reason to assume Garp and Roger were brothers.
