Nation is often considered a synonym for state. But a nation may exist with no border. The Welsh are a nation. Can a nation with no geographical connection be or own a state?
The answer largely depends on what you consider "State" and is basically definition dependent.
Wikipedia openly indicates that there's no clear definition:
There is no academic consensus on the most appropriate definition of the state. The term "state" refers to a set of different, but interrelated and often overlapping, theories about a certain range of political phenomena. The act of defining the term can be seen as part of an ideological conflict, because different definitions lead to different theories of state function, and as a result validate different political strategies. According to Jeffrey and Painter, "if we define the 'essence' of the state in one place or era, we are liable to find that in another time or space something which is also understood to be a state has different 'essential' characteristics" 
Some definitions don't impose a territorial/geographical aspect:
- (also State) a an organized political community under one government; a commonwealth; a nation. (Wikipedia citing Thompson, Della, ed. (1995). "state". Concise Oxford English Dictionary (9th ed.). Oxford University Press)
Yet, there are also definitions that impose a territorial requirement, including most common ones:
Under such definitions, "no territory" means "no state":
Speakers of American English often use the terms state and government as synonyms,[note 1] with both words referring to an organized political group that exercises authority over a particular territory. (Wikipedia).
The most commonly used definition is Max Weber's, which describes the state as a compulsory political organization with a centralized government that maintains a monopoly of the legitimate use of force within a certain territory
Another commonly accepted definition of the state is the one given at the Montevideo Convention on Rights and Duties of States in 1933. It defined state as a space that possess the following : A permanent population, a defined territory and a government that is capable of maintaining effective control over the corresponding territory and of conducting International relations with other states.
Examples of nations that are states without firm geographic delineations:
Many Native American tribes, while constituting nations, were rather geographically disbursed due to their culture (migratory hunting, e.g. on the Great Planes).
As an example, Lacota and other Sioux for example were all over the place, before displacing other tribes in the area of Black Hills (and even then were pretty geographically dispersed).
At that, Sioux Confederation can likely be considered a state - they had a government and soveregnity (to the point of US government conducting treaties with them).
One may quibble that ISIS (Islamic State of Iraq and Syria) qualifies. They are somewhat diffused, despite holding specific territory, yet are a state for now.
Of separate note, there's newer political theories that postulate less-territorial states, given humankind's development trajectory, in near future. They are partly based on the following factors:
Portable productivity. In the older days, you had to have a field to plow, and building to place your blacksmithy and a house to live in.
Ironically, that's precisely what allowed pre-agricultural Sioux to be a state without a defined territory - they were portable.
On the other extreme are people who can make a living while traveling - typically, various IP-producing types (journalists, creative types, programmers etc...) - and the more we move towards IP-based economy and post-scarcity society, the more this becomes feasible. Advent of 3d-printing improves the picture even more.
Increased ability for asymmetric warfare.
One factor that made territorial holdings important to a state is that holding territory allows one to amass the force needed to protect one's sovereignty, as far as economy, logistics, manpower and tactics.
Project into the future; where man-portable nuclear devices are possible as the least of dangers; and nano-warfare and cyber-warfare is possible; and don't require either territory or large autonomy.
As such, a territory-less nation that has access to such threats can protect their sovereignty against other nations.
Easier travel, largely tied to cheaper energy and better transportation.
Again, this benefits both types of extremes - pre-agricultural hunter/gatherer nomads, who need a horse (or two feet), a tent/backpack, and enough fodder. As well as more futuristic member of a nation who can buy a world-circumnavigating boat; or travel by land freely on any continent end to end reasonably cheaply and easily.