This question as it is written is loaded for a couple of reasons:
Firstly, if you are you asking if this is a Masonic gesture, consider that there are also many works of art where this gesture is done where the people involved are clearly not Masons. So it is wrong to suggest that this pose is "purely" a Masonic gesture and providing an answer to the question as is, is misleading.
Secondly, and this has come up before on this site, you are asking about a secret society who: operates in secret, passes traditions on via word of mouth and does not have a published guidebook which states clearly what they do.
However, there is a supposed* Masonic gesture where the right hand is placed inside the coat / shirt that appears quite similar to the above gesture. So the answer to your question is it is possible, but don't confuse that with meaning that everyone who does this in a portrait is a Mason or is copying a Mason.
Other possible valid explanations:
- It is a gesture to make the person look more stately or civilised
- It was one of the ways a person could rest their hands during a long portrait
- It was a common gesture in that period for portraits (in 500 years time people could be asking why do so many kids do the peace sign in photographs)
From Duncan's Masonic Ritual and Monitor
by Malcolm C. Duncan 
My words are Shem, Japhet, and Adoniram; my sign is this: (thrusting
his hand in his bosom); it is in imitation of one given by God to
Moses, when He commanded him to thrust his hand into his bosom, and,
taking it out, it became as leprous as snow. My word of exhortation is
explanatory of this sign, and is found in the writings of Moses, viz.,
fourth chapter of Exodus:
"And the Lord said unto Moses, Put now thine hand into thy
bosom. And he put his hand into his bosom; and when he took it out,
behold, his hand was leprous as snow,".
FIG. 34. SIGN OF THE MASTER OF THE SECOND VEIL.
*In reference to the authenticity of this book or details within, refer to my second point above; this is a secret society. Furthermore rituals in one geographical area may only be for that limited area and not for the entire organisation or even at the country level for that matter.
Because of the reasons above it is not possible to make an accurate assumption about the Masons and say "oh yeah, this is something the Masons do". There is no evidence available to suggest that this is an organisation wide gesture. There is zero evidence to suggest that everyone who is doing this is making a Masonic symbol.