This is a question I saw posted in the Lolita Fashion Mentoring group on FaceBook. Here's my take on it as a Goth.
Short answer: no. Long answer: sort of...
Gothic Lolita is one of the older subsets of Lolita and is a fashion that applies the Gothic aesthetic to the Lolita template.
As a fashion, it is certainly Gothic, as the name states, and takes its inspiration from a lot of the same sources as the subset of Goth fashion that is Romantic Goth. Inspiration has gone both ways between Gothic Lolita and Romantic Goth, especially in recent years, and aesthetically they are very closely linked. Both include ruffles, lace, a lot of black and a taste for anachronism, a tendency towards more modest fashion, full skirts, and details from traditional Gothic imagery.
An aside: I would say that Romantic Goth has suffered in the past from a lot of poor-quality clothes involving cheap, scratchy lace, bad quality velvet and satin, and designs that err towards Hallowe'en vampire and witch costumes, but it seems that in the last 5 years or so, the quality has improved, and the standard has raised, probably partly through social media making it easier for models, photographers and designers to showcase what truly stunning Romantic Goth fashion can look like, thus inspiring the rest of us. Quality is something that is stressed in all forms of Lolita, and I am glad to see this attitude being taken up amongst Goths too.
In talking about Gothic Lolita's connection to Goth, an easy place to look at is the fashion designer at Gothic Lolita brand Moi-même-Moitié and musician, having played with Malice Mizer and Moi-dix-Moits Mana. Malice Mizer, original band of Mana, started off with a sound that included a distinct edge of the '80s Goth sound. The style of his rather influential brand - which he named Elegant Gothic Lolita and Elegant Gothic Aristocrat - has certainly taken a lot from the Goth aesthetic. A lot of the early images from the brand, modelled by a cross-dressing Mana, include having teased hair, very large platform shoes, ghostly makeup and dramatic eye-liner, elements which are very distinctly Goth, and have since fallen out of the Gothic Lolita aesthetic, but are still common in the Goth aesthetic.
Gothic Lolita, however, is much broader than the brand Moi-même-Moitié, as there have been Gothic pieces brought out by plenty of other brands, and the now-infamous black and white colour scheme having had an enduring popularity. Lolita also pre-exists Gothic Lolita, and its earlier incarnations had very little of anything Gothic about them at all.
Gothic Lolita is also primarily a fashion choice and Lolita a fashion-based subculture, and in that diverges significantly from the Goth subculture, as the Goth subculture is more than just its fashion aspect and places a huge importance on its musical roots and wider creative and cultural aspects. Gothic Lolita is certainly not tied to the same bands and music as Goth, is not even as closely tied, at least in its incarnations outside of Japan, to Mana and Visual Kei music.
Aesthetically, the two fashions are related and compatible, and inter-compatible if you want to mix things up (even though at this point it won't be considered Lolita as Lolita means adhering to the template of 'the rules') but they are not the same subculture. They are not mutually exclusive subcultures. It is utterly possible to dress in Gothic Lolita, go to Lolita meet-ups and tea-parties and be active in that subculture and also be active as a Goth; in fact, that's what I'm trying to do, although I don't intend to dress exclusively in Lolita.
In short, Goth is a subculture that is quite broadly a subculture with a lot more to it than just fashion, and Lolita is a subculture that is primarily about fashion. Gothic Lolita is applying the aesthetic of Goth to the fashion template of Lolita, and as such bridges the gap to a degree. Dressing in Gothic Lolita does not inherently make one Goth, as one would need to participate in the broader Goth subculture, and being Goth does not exclude one from dressing in Gothic Lolita.