We'll never know, but statistically speaking, it is pretty likely as any number of studies show that while it isn't universal, it is an activity that the vast majority of men partake in at some point or other.

As for how he held himself out to others... well, he certainly tried to make it seem like something that was below him. August Kubizek, one of the few friends that Hitler had in during his late teens/early 20s, and his roommate in 1908, recalled that Hitler would talk about sex endlessly during many evening chats, particularly:

on the need for sexual purity to protect what he grandly called the 'flame of life'

While not explicitly saying "masturbation", I don't think we'd be wrong to say that act perhaps would fall afoul of "sexual purity". He also would rant about sexual "depravity" in general, having plenty to say about prostitutes - members of the German race had no business risking disease with them, prostitutes we only for the "inferior races" - and homosexuals as well. He had an 'idealized' love, "Stephanie" while a boy in Linz, but it was purely a love from afar and he never told her. According to Kershaw, examining all the evidence, at the very least we can safely assume Hitler had no sexual experience through his mid-20s, as there is simply no evidence of a woman in his life, and the one account of him resorting to prostitutes is "baseless". During the war, his apparent lack of sexual interest was one means his comrades poked fun at him, once asking if he was using time in the rear to 'look for a Mamsell', to which he replied "I'd die of shame looking for sex with a French girl".

There really is no facet of Hitler that hasn't been scrutinized by many, many people, and his sexuality is a popular one, but at the same time one of the hardest to be certain about since he he left little private writing, and wasn't lying on a couch with a doctor taking notes about his childhood. So we get rumors about incest (with his niece specifically) and a penchant for BDSM on the one hand (Many of the purient stories I believe can be traced to Otto Strasser slinging mud. While he knew Hitler well, he also had serious bones to pick), and a dislike of any physical contact, a fear of women not to mention total lack of respect for them, and a simple inability to be close with anyone. Putzi Hanfstaengl was convinced that Hitler was simply impotent, and his public speaking was essentially a replacement sexual act for him (Hitler once professed his undying love for Putzi's wife Helene, but they both believed him to be "acting out a role [of the] languishing troubadour".

What few relations he did have with women were, many believe, more about power than sex, as it was all with young, impressionable girls many years his junior - Maria Reiter was 21 years younger, Geli Raubal 19, and Eva Braun 23 years younger. Simply put, as with all his relationships with people, he wanted to be around someone who gave him full deference and be in awe. When young he described is deal woman as, among other traits, "stupid". The relationship he had with his niece Geli is, of course, the most salacious one to dwell on, and as Kershaw notes, we simply can't know if it was actually sexual, but what evidence we do have points to it being the closest thing he had to being "emotionally dependent on a woman". As for his relation with Braun, his photographer noted:

To him she was just an attractive little thing, in whom, in spite of her inconsequential and feather-brained outlook - or perhaps just because of it - he found the type of relaxation and repose he sought. But never, in voice, look,or gesture, did he ever behave in a way that suggested any deeper interest in her.

So anyways, I turned this more into a general examination of Hitler's sexuality than his onanistic habits, but the simple fact is we don't know, and I feel that looking at it more generally is the only way to have any sort of picture to judge for yourself with. The sum of it is, that in interacting with others, he was clearly obsessed with the need for sexual purity and if he was asked, he certainly would have said "No!". In private too, he seems to have been, if not repulsed by sex, at least fearful of the concept. He was quite misogynistic toward women in his views on them as the inferior sex, and while he had a few relationships with women, we don't know if they were sexual or not, but can say that an important component was the power imbalance he held in them.

All cited to Ian Kershaw, Hitler: 1889-1936 Hubris