Hugely, and it wasn't just the grain: Egypt was the economic backbone of the Roman empire.

The country was quite naturally wealthy, with substantial gold and emerald mines, large scale quarries, and a massive conduit through the centre of the region: the Nile River. These, obviously, were a superb base for the land as a whole, and enabled the city of Alexandria to reach the heights that it did in Antiquity. Egypt's natural positioning, though, was just as important, if not more so: not only was Alexandria well positioned as a trade port for the Eastern Mediterranean, not only was it enabled by the Nile, but Egypt also was a major trade crossroad.

Now, this is where most people zone out. Trade is a delightful concept that you flip past to get to the actual important stuff, but here I'll ask you to just read a little bit on this topic. You see, Egypt provided the Roman Empire with ports on the Red Sea, allowing for their previously Mediterranean-focused trade to go global. Ships departed Egypt for ports along the East coast of Africa, for the marvelous perfumed lands of Arabia, and for the Orient - the ships that went to India were massive freighters that shipped and returned massive quantities of goods. The Indian Ocean trade was Big Business by definition. Here's a starter to give you an idea - this is the Muziris Papyrus, which is a business contract on one side, and a list of goods being shipped on the other:

Front:

[ - - - ] your other administrators or managers, and on agreement(?) [I will give?] to your(?) camel-driver - - - - - (?) for the extra charges [of the journey] to Koptos, and I will convey (the goods) through the desert under guard and protection [up to the] public tax-receiving warehouses at Koptos, and [I will] place them under the [authourity] and seal of yourself, or of your administrators or whichever one of them is present, until their loading at the river, and I will load them [at the requi]red time onto a safe ship on the river, and I will convey them down to the warehouse for receiving the quarter-tax [at Alex]andria, and [likewise] will place them under the authourity and seal of yourself or your men for(?) all the payments [for the ship(?)] from now to collection of the quarter-tax, and of(?) the desert tran[sport] and the carrying-charges of the river-workers and the other incidental(?) exp[ens]es < - - - > on occurence of the date for repayment specified in the contracts of lo[an] for (the trip to) Muziris.

If I do not [then] duly discharge the aforesaid loan in my name, that then [you] and your administrators or manangers are to have the option and com[plete] authourity, if you so choose, to carry out execution without [notifica]tion or summons to judgement, to possess and own the afore[said] security and pay the quarter-tax, to convey the [three] parts which will be left where you choose and to sell or use them as security [and] to transfer them to another person, if you so choose, and to deal with the items of the security in whatsoever way you choose, and to buy them for yourself at the price current at the time, and to subtract and reckon in what falls due [on account of the aforesai]d loan, on terms that the responsibility for what falls due [lies] with you and your administrators or managers and we are free from accus[at]ion in every respect, and that the surplus or shortfall from the capital [goes] to me the borrower and giver of sec[urity] [ - - - - - - ]

Back (TL;DR of cashflow at the bottom):

Gangetic Nard: 60 boxes, of which likewise the price is reckoned with the box at 4,500 dr. of silver, 45 tal.
Ivory: first (A), sound: 78 talents-weight 54 1/2 minai, of which likewise the price is reckoned, first (A1) 78 tal-weight 43 minai, which become by the standards of the quarter-tax, the talent being reckoned at 95 lbs, 7478 lbs, from which the equivalent is, reckoning, <[unclear]> lbs to the talent, on the ratio which is normally reckoned among merchants.
76 tal-weight 41 minai, with the mina at 100 dr., total 76 tal 4100 dr. Then the remaining tusks (A2), taken at the higher (weight) by the arabarchs for the collection of the quarter-tax in the sum of tusks despite the equivalence when undergoing the collection of the quarter-tax, 11 1/2 with the mina at the same 100 dr., 1175 dr (of silver).
Makes total 76 tal. 5275 dr.
Then (B) fragments [probably fabric]: 13 tal-weight 9/12 1/4 minai, of which likewise the price is reckoned, first (B1), 12 tal-weight 47 mn., which, as explained above, become in turn(?) by the standards of the quarter-tax 1214 lbs, and, according to how among the merchants it is reckoned, (are) 12 tal-weight 27 mn, with the mna at 70 dr., 8 tal 4290 dr. of silver.
Then (B2), the remaining (fragments), taken at a higher (weight) for collection of the quarter-tax, as explained above, 22 1/2 1/4 mn., with the mna at the same 70 dr., 1592 1/2 dr. of silver.
Total for fragments: 8 tal., 5882 1/2 dr
Total price of ivory [85 tal 5157 1/2 dr] of silver.
Makes the price of the 3 parts of the cargoes shipped out in the ship 'Hermapollon'
1154 tal. 2852 dr. of silver

The converted valuation here is about 7,000,000 sesterces after tax - ~7000 kilograms of silver. That's an insane amount of wealth, and that was just one ship. And it apparently didn't even have cinnamon or pepper on it. Pepper alone became such a major commodity that it was affordable by most people in the Roman world - while not necessarily an indication of the purchasing power of the poor, it's noticable that most of Apicius' recipes in his cookbook involved pepper. But there's a note here that you might have skipped over! The number I gave above was after the tax had been deducted. The standard customs tax in the Roman empire was called the tetartei - or the "quarter" tax. That was quite literal: It was a 25% tariff. This one shipment, which is generally considered to be pretty average, was one of at least 100, if not 200, and brought in about 2.3 million sesterces. You extrapolate that and the Roman Empire funded over a third of its military from the Indian trade through Egypt alone, not counting anything else. (Source on these numbers is Andrew Wilson in "Red Sea Trade and the State," in Across the Ocean: Nine Essays on Indo-Mediterranean Trade)

How did this affect the food? Well, it revolutionized it, as I noted above. Spices were in heavy demand, as you can imagine - today, salt and pepper are base spices for anything, and the Romans very much felt the same way! Imported spices made food far more interesting - even if some (such as cinnamon) were priced to such incredible degrees that most people just made do with knockoffs. Not only did this trade keep the Roman empire moving, but it also kept the people satisfied - and in an empire where the bellies of the city of Rome often dictated Imperial policy, that was important.