First, to answer your question. Yes, I agree with other posters, you can add no expiry once you get to the park. You can do it at any guest services or resort desk. We have done this before. You can also add days.
Second, there is a lot of emotional value in adding no expiry, even if it isn't a great deal financially (which it can be). We have done exactly what you propose for years and I LOVE the thought that I always have an extra 2 or 3 Disney days in my pocket for whenever we can drive down for a quick visit.
Disney has changed the way no expiry is priced, and it is no longer the killer deal it used to be. But, it can still save some money.
You already have a 7 day ticket. It will cost an additional $110 to add no expiry to your current tickets. For $209 more you can make it a 10-day ticket with no expiry ($9 for the three extra days and $200 for the no expiry). However, with the added cost for 10 day no expiry, you won't save as much as if you stick with your 7 day tickets and add no expiry. The table below assumes you will want park hopper on future visits when comparing the future ticket price. And, it doesn't factor in price increases, which your no expriy can guard against.
Add no expiry on 7 days $110
...............................Future Ticket Price.....Savings due to no expiry
Use 3d with 4 left............$269...............................$159
Use 4d with 3 left............$262...............................$152
Use 5d with 2 left............$199...............................$89
Use 6d with 1 left............$125...............................$15
Add 3 days and no expiry $209
...............................Future Ticket Price.....Savings due to no expiry
Use 3d with 7 left............$278...............................$69
Use 4d with 6 left............$275...............................$66
Use 5d with 5 left............$272...............................$63
Use 6d with 4 left............$269...............................$60
There is one more consideration. If you only use 3 days and are close enough to come back for quick visits, adding 3 days with no expiry will give you SEVEN leftover days, which for us would mean TWO trips - a 3-day and a 4-day. If, in the future, you bought a 3-day ticket and then a 4-day ticket, this would cost $531! So adding the 3 days with no expiry saves you $322! Now THAT's a good deal!!!
I've been pondering this for our future visits, so your question gave me a good excuse to look up prices and work it out.